diff --git a/core/src/lib.rs b/core/src/lib.rs
index 22dd198..e2218f3 100644
--- a/core/src/lib.rs
+++ b/core/src/lib.rs
@@ -9,6 +9,7 @@
 #![feature(unsize)]
 #![feature(coerce_unsized)]
 #![feature(option_into_flat_iter)]
+#![feature(const_index)]
 
 #[cfg(feature = "layout-diagnostics")]
 pub mod layout_diagnostics;
diff --git a/core/src/orientation/align.rs b/core/src/orientation/align.rs
index 1ce2dd6..6a10cc6 100644
--- a/core/src/orientation/align.rs
+++ b/core/src/orientation/align.rs
@@ -1,3 +1,4 @@
+use crate::util::impl_axis_index;
 use crate::{Px, Rel};
 
 use super::*;
@@ -89,20 +90,6 @@ impl RegionAlign {
         x: AxisAlign::NEG,
         y: AxisAlign::NEG,
     };
-
-    pub fn axis(&self, axis: Axis) -> AxisAlign {
-        match axis {
-            Axis::X => self.x,
-            Axis::Y => self.y,
-        }
-    }
-
-    pub fn axis_mut(&mut self, axis: Axis) -> &mut AxisAlign {
-        match axis {
-            Axis::X => &mut self.x,
-            Axis::Y => &mut self.y,
-        }
-    }
 }
 
 impl RegionAlign {
@@ -231,3 +218,5 @@ impl RegionAlign {
         UiVec2::from(self)
     }
 }
+
+impl_axis_index!(RegionAlign => AxisAlign);
diff --git a/core/src/orientation/axis.rs b/core/src/orientation/axis.rs
index 279484d..7e73f41 100644
--- a/core/src/orientation/axis.rs
+++ b/core/src/orientation/axis.rs
@@ -1,4 +1,5 @@
 use super::*;
+use crate::util::impl_axis_index;
 use crate::{Fixed, FixedVec2};
 
 #[derive(Copy, Clone, Debug, Eq, PartialEq)]
@@ -53,20 +54,6 @@ pub enum Sign {
 }
 
 impl<const SHIFT: u32> FixedVec2<SHIFT> {
-    pub const fn axis(&self, axis: Axis) -> Fixed<SHIFT> {
-        match axis {
-            Axis::X => self.x,
-            Axis::Y => self.y,
-        }
-    }
-
-    pub const fn axis_mut(&mut self, axis: Axis) -> &mut Fixed<SHIFT> {
-        match axis {
-            Axis::X => &mut self.x,
-            Axis::Y => &mut self.y,
-        }
-    }
-
     pub const fn from_axis(axis: Axis, aligned: Fixed<SHIFT>, ortho: Fixed<SHIFT>) -> Self {
         match axis {
             Axis::X => Self::new(aligned, ortho),
@@ -76,20 +63,6 @@ impl<const SHIFT: u32> FixedVec2<SHIFT> {
 }
 
 impl Vec2 {
-    pub fn axis(&self, axis: Axis) -> f32 {
-        match axis {
-            Axis::X => self.x,
-            Axis::Y => self.y,
-        }
-    }
-
-    pub fn axis_mut(&mut self, axis: Axis) -> &mut f32 {
-        match axis {
-            Axis::X => &mut self.x,
-            Axis::Y => &mut self.y,
-        }
-    }
-
     pub const fn from_axis(axis: Axis, aligned: f32, ortho: f32) -> Self {
         Self {
             x: match axis {
@@ -148,3 +121,6 @@ impl<T> BothAxis<T> {
         }
     }
 }
+
+impl_axis_index!({const SHIFT: u32} FixedVec2<SHIFT> => Fixed<SHIFT>);
+impl_axis_index!(Vec2 => f32);
diff --git a/core/src/orientation/len.rs b/core/src/orientation/len.rs
index cd6059e..c272467 100644
--- a/core/src/orientation/len.rs
+++ b/core/src/orientation/len.rs
@@ -1,4 +1,5 @@
 use super::*;
+use crate::util::impl_axis_index;
 use crate::{Px, PxVec2, Rel, UiNum, Weight, util::impl_op};
 
 #[derive(Debug, Default, Clone, Copy, PartialEq)]
@@ -118,20 +119,6 @@ impl Size {
             },
         }
     }
-
-    pub fn axis(&self, axis: Axis) -> LayoutLen {
-        match axis {
-            Axis::X => self.x,
-            Axis::Y => self.y,
-        }
-    }
-
-    pub fn axis_mut(&mut self, axis: Axis) -> &mut LayoutLen {
-        match axis {
-            Axis::X => &mut self.x,
-            Axis::Y => &mut self.y,
-        }
-    }
 }
 
 impl LayoutLen {
@@ -158,11 +145,32 @@ impl LayoutLen {
         Len::from_parts(self.rel.add(share), self.px)
     }
 
+    /// Only pixels: the same number of them whatever box it lands in, and
+    /// whatever anyone else in the row asks for. A length that is any part
+    /// of a box or of what is left over is not one.
+    pub fn is_px(self) -> bool {
+        self.rel == Rel::ZERO && self.leftover == Weight::ZERO
+    }
+
+    /// Nothing but a claim on what is left over, so there is no length here
+    /// at all where nothing is.
+    pub fn is_only_leftover(self) -> bool {
+        self.leftover > Weight::ZERO && self.without_leftover() == Len::ZERO
+    }
+
+    /// What this takes whatever is left over: the reading of a length for
+    /// anyone not dividing a box between siblings, where a share is a claim
+    /// on someone else's room rather than a length of its own.
+    /// [`Self::apply_leftover`] is the opposite reading of the same value.
+    pub const fn without_leftover(self) -> Len {
+        Len::from_parts(self.rel, self.px)
+    }
+
     /// This length, given as a part of a box `len` long, as a part of the
     /// box `len` is itself a part of. The share is untouched: it is a claim
     /// on whoever divides the room, not a fraction of anything.
     pub const fn within_len(self, len: Len) -> Self {
-        let part = Len::from_parts(self.rel, self.px).within_len(len);
+        let part = self.without_leftover().within_len(len);
         Self {
             px: part.px,
             rel: part.rel,
@@ -236,3 +244,5 @@ impl std::fmt::Display for LayoutLen {
         Ok(())
     }
 }
+
+impl_axis_index!(Size => LayoutLen);
diff --git a/core/src/orientation/pos.rs b/core/src/orientation/pos.rs
index ca6be56..fa9fd8a 100644
--- a/core/src/orientation/pos.rs
+++ b/core/src/orientation/pos.rs
@@ -1,3 +1,4 @@
+use crate::util::impl_axis_index;
 use std::{fmt::Display, marker::Destruct};
 
 use super::*;
@@ -61,20 +62,6 @@ impl UiVec2 {
         }
     }
 
-    pub fn axis_mut(&mut self, axis: Axis) -> &mut Len {
-        match axis {
-            Axis::X => &mut self.x,
-            Axis::Y => &mut self.y,
-        }
-    }
-
-    pub fn axis(&self, axis: Axis) -> Len {
-        match axis {
-            Axis::X => self.x,
-            Axis::Y => self.y,
-        }
-    }
-
     /// Resolved against a box of `size`, which is where a fraction stops
     /// being one and becomes a place.
     pub fn to_px(&self, size: PxVec2) -> PxVec2 {
@@ -294,6 +281,15 @@ impl UiSpan {
         }
     }
 
+    /// A box `len` long inside this one, on the side `align` says. Both must
+    /// be lengths of the same rel base: it subtracts one from the other
+    /// rather than composing it in, which is what keeps a fraction the same
+    /// fraction however long this box turns out to be.
+    pub const fn place(self, len: Len, align: AxisAlign) -> Self {
+        let start = self.start + (self.len() - len).scale(align.rel());
+        Self::new(start, start + len)
+    }
+
     pub const fn len(&self) -> Len {
         self.end - self.start
     }
@@ -348,20 +344,6 @@ impl UiRegion {
             y: self.y.within(&parent.y),
         }
     }
-    pub const fn axis(&self, axis: Axis) -> &UiSpan {
-        match axis {
-            Axis::X => &self.x,
-            Axis::Y => &self.y,
-        }
-    }
-
-    pub const fn axis_mut(&mut self, axis: Axis) -> &mut UiSpan {
-        match axis {
-            Axis::X => &mut self.x,
-            Axis::Y => &mut self.y,
-        }
-    }
-
     pub const fn flip(&mut self, axis: Axis) {
         match axis {
             Axis::X => self.x.flip(),
@@ -462,3 +444,6 @@ impl Display for PixelRegion {
         write!(f, "{} -> {}", self.top_left, self.bot_right)
     }
 }
+
+impl_axis_index!(UiVec2 => Len);
+impl_axis_index!(UiRegion => UiSpan);
diff --git a/core/src/ui/holds.rs b/core/src/ui/holds.rs
index 067ef31..a9791f8 100644
--- a/core/src/ui/holds.rs
+++ b/core/src/ui/holds.rs
@@ -33,6 +33,12 @@ impl Holds {
         len.raw() >= self.lo.raw() && len.raw() <= self.hi.raw()
     }
 
+    /// Every length `other` holds for is one this holds for, so a drawing
+    /// made under this range is still good wherever `other` is.
+    pub const fn covers(self, other: Self) -> bool {
+        self.lo.raw() <= other.lo.raw() && self.hi.raw() >= other.hi.raw()
+    }
+
     pub const fn and(self, other: Self) -> Self {
         Self {
             lo: self.lo.max(other.lo),
diff --git a/core/src/ui/layout_holds.rs b/core/src/ui/layout_holds.rs
index 3a1a494..7ba7e3b 100644
--- a/core/src/ui/layout_holds.rs
+++ b/core/src/ui/layout_holds.rs
@@ -1,10 +1,12 @@
-use crate::{Axis, Holds, Len, PxVec2, UiRegion, UiVec2};
+use crate::util::impl_axis_index;
+use crate::{Axis, Holds, Len, Px, PxVec2, UiRegion, UiVec2};
 
 const AXES: [Axis; 2] = [Axis::X, Axis::Y];
 
-/// What one evaluation of a widget depends on: the window lengths its reads
-/// hold for, the pixel lengths of its own box, and the symbolic lengths of
-/// that box and of its rel base where either one is what it was expressed in.
+/// What one evaluation of a widget depends on along one axis: the window
+/// lengths its reads hold for, the pixel lengths of its own box, and the
+/// symbolic lengths of that box and of its rel base where either one is what
+/// it was expressed in.
 ///
 /// The symbolic lengths are pins rather than ranges: a container places its
 /// children as lengths of its rel base measured from where its own box starts,
@@ -19,61 +21,89 @@ const AXES: [Axis; 2] = [Axis::X, Axis::Y];
 /// of the rel base that is only pixels is not one: it is that many pixels
 /// whatever the rel base turns out to be.
 #[derive(Clone, Copy, Debug, PartialEq)]
+pub struct AxisHolds {
+    pub window: Holds,
+    pub rel_base: Option<Len>,
+    pub region: Holds,
+    pub region_len: Option<Len>,
+}
+
+impl AxisHolds {
+    pub const ANY: Self = Self {
+        window: Holds::ANY,
+        rel_base: None,
+        region: Holds::ANY,
+        region_len: None,
+    };
+
+    pub fn and(self, other: Self) -> Self {
+        // Two pins of the same length disagreeing would mean one drawing was
+        // a fraction of two different lengths at once.
+        debug_assert!(
+            self.region_len.is_none()
+                || other.region_len.is_none()
+                || self.region_len == other.region_len
+        );
+        debug_assert!(
+            self.rel_base.is_none() || other.rel_base.is_none() || self.rel_base == other.rel_base
+        );
+        Self {
+            window: self.window.and(other.window),
+            rel_base: self.rel_base.or(other.rel_base),
+            region: self.region.and(other.region),
+            region_len: self.region_len.or(other.region_len),
+        }
+    }
+
+    pub fn covers(self, other: Self) -> bool {
+        self.window.covers(other.window)
+            && self.region.covers(other.region)
+            && self
+                .region_len
+                .is_none_or(|len| other.region_len == Some(len))
+            && self.rel_base.is_none_or(|len| other.rel_base == Some(len))
+    }
+
+    /// Whether a widget in a box `len` long, with that rel base, in that
+    /// window, is one this drawing holds for.
+    pub fn contains(self, window: Px, rel_base: Len, len: Len) -> bool {
+        self.window.contains(window)
+            && self.rel_base.is_none_or(|pinned| pinned == rel_base)
+            && self.region.contains(len.to_px(window))
+            && self.region_len.is_none_or(|pinned| pinned == len)
+    }
+}
+
+/// [`AxisHolds`] on both axes. Every question asked of it is asked of one
+/// axis at a time, since a widget that read one length holds for any length
+/// of the other.
+#[derive(Clone, Copy, Debug, PartialEq)]
 pub struct LayoutHolds {
-    pub window: [Holds; 2],
-    pub rel_base: [Option<Len>; 2],
-    pub region: [Holds; 2],
-    pub region_len: [Option<Len>; 2],
+    pub x: AxisHolds,
+    pub y: AxisHolds,
 }
 
 impl LayoutHolds {
     pub const ANY: Self = Self {
-        window: [Holds::ANY; 2],
-        rel_base: [None; 2],
-        region: [Holds::ANY; 2],
-        region_len: [None; 2],
+        x: AxisHolds::ANY,
+        y: AxisHolds::ANY,
     };
 
     pub fn and(self, other: Self) -> Self {
-        let mut result = Self::ANY;
-        for n in 0..2 {
-            result.window[n] = self.window[n].and(other.window[n]);
-            result.region[n] = self.region[n].and(other.region[n]);
-            debug_assert!(
-                self.region_len[n].is_none()
-                    || other.region_len[n].is_none()
-                    || self.region_len[n] == other.region_len[n]
-            );
-            debug_assert!(
-                self.rel_base[n].is_none()
-                    || other.rel_base[n].is_none()
-                    || self.rel_base[n] == other.rel_base[n]
-            );
-            result.region_len[n] = self.region_len[n].or(other.region_len[n]);
-            result.rel_base[n] = self.rel_base[n].or(other.rel_base[n]);
+        Self {
+            x: self.x.and(other.x),
+            y: self.y.and(other.y),
         }
-        result
     }
 
     pub fn covers(self, other: Self) -> bool {
-        (0..2).all(|n| {
-            self.window[n].lo <= other.window[n].lo
-                && self.window[n].hi >= other.window[n].hi
-                && self.region[n].lo <= other.region[n].lo
-                && self.region[n].hi >= other.region[n].hi
-                && self.region_len[n].is_none_or(|len| other.region_len[n] == Some(len))
-                && self.rel_base[n].is_none_or(|len| other.rel_base[n] == Some(len))
-        })
+        self.x.covers(other.x) && self.y.covers(other.y)
     }
 
     pub fn contains(self, window: PxVec2, rel_base: UiVec2, region: UiRegion) -> bool {
-        AXES.into_iter().all(|axis| {
-            let n = axis as usize;
-            let len = region.axis(axis).len();
-            self.window[n].contains(window.axis(axis))
-                && self.rel_base[n].is_none_or(|pinned| pinned == rel_base.axis(axis))
-                && self.region[n].contains(len.to_px(window.axis(axis)))
-                && self.region_len[n].is_none_or(|pinned| pinned == len)
-        })
+        AXES.into_iter()
+            .all(|axis| self[axis].contains(window[axis], rel_base[axis], region[axis].len()))
     }
 }
+
+impl_axis_index!(LayoutHolds => AxisHolds);
diff --git a/core/src/ui/painter.rs b/core/src/ui/painter.rs
index 489ff39..ba174e3 100644
--- a/core/src/ui/painter.rs
+++ b/core/src/ui/painter.rs
@@ -3,7 +3,7 @@ use crate::layout_diagnostics::{self as diag, Counter};
 use crate::{
     Axis, Holds, LayoutHolds, LayoutLen, Len, PlaceDesc, Px, PxVec2, RegionAlign, Rel,
     RenderedText, RetainedPrimitive, Size, StrongWidget, TextAttrs, TextBuffer, TextData,
-    TextureHandle, UiRegion, UiRenderState, UiRsc, UiSpan, UiVec2, Weight, WidgetId, Widgets,
+    TextureHandle, UiRegion, UiRenderState, UiRsc, UiVec2, Weight, WidgetId, Widgets,
     render::{
         GlyphPrimitive, Mask, MaskIdx, MoveIdx, Primitive, PrimitiveInst, PrimitiveKind,
         TexturePrimitive,
@@ -157,10 +157,10 @@ impl<'a> Painter<'a> {
     /// only moves its child does not pin its drawing to a rel base.
     fn state_rel_base(&mut self, mut place: PlaceDesc) -> PlaceDesc {
         for axis in AXES {
-            if let Some(span) = place.axis(axis).narrows_rel_base() {
+            if let Some(span) = place[axis].narrows_rel_base() {
                 let len = span.len();
                 let stated = (len != Len::FULL).then(|| len.within_len(self.rel_base(axis)));
-                *place.axis_mut(axis) = place.axis(axis).with_rel_base(stated);
+                place[axis] = place[axis].with_rel_base(stated);
             }
         }
         place
@@ -186,7 +186,7 @@ impl<'a> Painter<'a> {
         let declared = self.declared_lens(id);
         let align = self.rsc.widgets().alignment(id.id());
         let (rel_base, region) =
-            rel_base_and_region(self.region, self.rel_base, place, declared, align);
+            place.rel_base_and_region(self.region, self.rel_base, declared, align);
         #[cfg(feature = "layout-diagnostics")]
         if region_node {
             diag::bump(Counter::RegionNodeDraws);
@@ -258,7 +258,7 @@ impl<'a> Painter<'a> {
         let place = self.state_rel_base(place.into());
         let states_rel_base = AXES
             .iter()
-            .any(|&axis| place.axis(axis).stated_rel_base().is_some());
+            .any(|&axis| place[axis].stated_rel_base().is_some());
         if states_rel_base || !self.children.contains(&id.id()) {
             return self.widget_at(id, place);
         }
@@ -293,7 +293,7 @@ impl<'a> Painter<'a> {
     /// that comes of them is kept on the child, and `redraw` compares it
     /// there.
     fn declared_lens<W: ?Sized>(&self, id: &StrongWidget<W>) -> [Option<LayoutLen>; 2] {
-        declared_lens(self.rsc.widgets(), id.id())
+        self.rsc.widgets().declared_lens(id.id())
     }
 
     /// What a child says its length is without being drawn, if it can say,
@@ -304,12 +304,12 @@ impl<'a> Painter<'a> {
         let widgets = self.rsc.widgets();
         // A rule is the answer where there is one: it wins over whatever the
         // widget would draw, so it has to win over what the widget says too.
-        let hint = widgets.size_rules(id.id()).axis(axis).exact().or_else(|| {
+        let hint = widgets.size_rules(id.id())[axis].exact().or_else(|| {
             widgets
                 .get_dyn(id.id())
                 .and_then(|widget| widget.size_hint(axis))
         });
-        let rel_base = self.rel_base.axis(axis);
+        let rel_base = self.rel_base[axis];
         let resolved = hint.map(|hint| hint.within_len(rel_base));
         #[cfg(feature = "layout-diagnostics")]
         {
@@ -326,7 +326,7 @@ impl<'a> Painter<'a> {
             // the child's own: resolved against a rel base of pixels, none is
             // left to see it by.
             if hint.rel != Rel::ZERO {
-                self.own.rel_base[axis as usize] = Some(rel_base);
+                self.own[axis].rel_base = Some(rel_base);
             }
         }
         resolved
@@ -392,8 +392,8 @@ impl<'a> Painter<'a> {
     /// again. One axis at a time, because a container that divides one axis
     /// holds for any length of the other.
     pub fn region_len(&mut self, axis: Axis) -> Len {
-        let len = self.region.axis(axis).len();
-        self.own.region_len[axis as usize] = Some(len);
+        let len = self.region[axis].len();
+        self.own[axis].region_len = Some(len);
         len
     }
 
@@ -403,8 +403,8 @@ impl<'a> Painter<'a> {
     /// Reading it pins the drawing to that rel base, the way
     /// [`Self::region_len`] pins it to the box.
     pub fn rel_base(&mut self, axis: Axis) -> Len {
-        let len = self.rel_base.axis(axis);
-        self.own.rel_base[axis as usize] = Some(len);
+        let len = self.rel_base[axis];
+        self.own[axis].rel_base = Some(len);
         len
     }
 
@@ -425,10 +425,7 @@ impl<'a> Painter<'a> {
     /// worth anything, since reading one is also what makes its own size
     /// depend on it.
     pub fn has_exact_size(&self, axis: Axis) -> bool {
-        self.rsc
-            .widgets()
-            .size_rules(self.id)
-            .axis(axis)
+        self.rsc.widgets().size_rules(self.id)[axis]
             .exact()
             .is_some()
     }
@@ -442,9 +439,9 @@ impl<'a> Painter<'a> {
     /// One axis of this widget's own box in pixels. Prefer this to
     /// [`Self::px_size`] when the other axis cannot affect the drawing.
     pub fn px_len(&mut self, axis: Axis) -> Px {
-        let len = self.region.axis(axis).len();
-        let px = len.to_px(self.window.axis(axis));
-        let own = &mut self.own.region[axis as usize];
+        let len = self.region[axis].len();
+        let px = len.to_px(self.window[axis]);
+        let own = &mut self.own[axis].region;
         if *own == Holds::ANY {
             *own = Holds::at(px);
         }
@@ -456,15 +453,15 @@ impl<'a> Painter<'a> {
     /// of the box, and the same reported size. A widget that read its length
     /// in pixels holds for that one alone until it says otherwise.
     pub fn holds(&mut self, axis: Axis, holds: impl Into<Holds>) {
-        let len = self.region.axis(axis).len();
+        let len = self.region[axis].len();
         let holds = holds.into();
         debug_assert!(
-            holds.contains(len.to_px(self.window.axis(axis))),
+            holds.contains(len.to_px(self.window[axis])),
             "'{}' ({:?}) says its drawing holds for lengths that leave out its own box",
             self.label(),
             self.id
         );
-        self.own.region[axis as usize] = holds;
+        self.own[axis].region = holds;
     }
 
     /// A window length in pixels, which is what every length in layout is
@@ -472,9 +469,9 @@ impl<'a> Painter<'a> {
     /// length is a fraction of it; one that is only pixels is that many
     /// pixels in any window and pins nothing.
     pub fn to_px(&mut self, len: Len, axis: Axis) -> Px {
-        let window = self.window.axis(axis);
+        let window = self.window[axis];
         if len.rel != Rel::ZERO {
-            let own = &mut self.own.window[axis as usize];
+            let own = &mut self.own[axis].window;
             if *own == Holds::ANY {
                 *own = Holds::at(window);
             }
@@ -489,12 +486,12 @@ impl<'a> Painter<'a> {
     pub fn window_holds(&mut self, axis: Axis, holds: impl Into<Holds>) {
         let holds = holds.into();
         debug_assert!(
-            holds.contains(self.window.axis(axis)),
+            holds.contains(self.window[axis]),
             "'{}' ({:?}) says its drawing holds for windows that leave out this one",
             self.label(),
             self.id
         );
-        self.own.window[axis as usize] = holds;
+        self.own[axis].window = holds;
     }
 
     pub fn text_data(&mut self) -> &mut TextData {
@@ -553,7 +550,7 @@ impl<W: ?Sized> DrawResult<'_, '_, W> {
     }
 
     pub fn len(self, axis: Axis) -> LayoutLen {
-        self.size().axis(axis)
+        self.size()[axis]
     }
 }
 
@@ -606,16 +603,18 @@ impl Painter<'_> {
     ) -> LayoutHolds {
         let mut result = LayoutHolds::ANY;
         for axis in AXES {
-            let n = axis as usize;
+            let declared = declared[axis as usize];
+            let holds = holds[axis];
+            let result = &mut result[axis];
             // Every read became pixels against the window, so a range on
             // it is already in this widget's terms.
-            result.window[n] = holds.window[n];
-            let at = *place.axis(axis);
+            result.window = holds.window;
+            let at = place[axis];
             let reaches = at.stated_rel_base().is_none()
                 && !at.is_sized()
-                && declared[n].is_none_or(|len| len.rel != Rel::ZERO);
-            result.rel_base[n] = holds.rel_base[n].and(reaches.then(|| self.rel_base.axis(axis)));
-            match (at.within_span(), declared[n].is_some()) {
+                && declared.is_none_or(|len| len.rel != Rel::ZERO);
+            result.rel_base = holds.rel_base.and(reaches.then(|| self.rel_base[axis]));
+            match (at.within_span(), declared.is_some()) {
                 // Its box is a part of this widget's own box, in that box's
                 // own lengths, so what it holds for maps back through that
                 // part into a range on this widget's box. A length it pinned
@@ -625,10 +624,10 @@ impl Painter<'_> {
                 // widget's own length.
                 (Some(span), false) => {
                     let part_len = span.len();
-                    result.region[n] = holds.region[n].through(part_len);
-                    result.region_len[n] = holds.region_len[n].map(|pinned| match part_len.rel {
+                    result.region = holds.region.through(part_len);
+                    result.region_len = holds.region_len.map(|pinned| match part_len.rel {
                         Rel::ONE => pinned - Len::from_parts(Rel::ZERO, part_len.px),
-                        _ => self.region.axis(axis).len(),
+                        _ => self.region[axis].len(),
                     });
                 }
                 // Its box is a length this widget decided, from its own
@@ -636,8 +635,7 @@ impl Painter<'_> {
                 // widget's box reaches it, so what it holds for is a range
                 // on the window and none of it on that box.
                 _ => {
-                    result.window[n] =
-                        result.window[n].and(holds.region[n].through(region.axis(axis).len()));
+                    result.window = result.window.and(holds.region.through(region[axis].len()));
                 }
             }
         }
@@ -645,35 +643,40 @@ impl Painter<'_> {
     }
 }
 
-/// What a widget declares a length of its box to be. `leftover` is not one: a
-/// share of what is left over is only a length to the widget dividing one,
-/// so it passes up in the size instead.
-pub(crate) fn declared_lens(widgets: &Widgets, id: WidgetId) -> [Option<LayoutLen>; 2] {
-    let rules = widgets.size_rules(id);
-    let widget = widgets.get_dyn(id);
-    AXES.map(|axis| {
-        rules.axis(axis).declared().or_else(|| {
-            // A hint still narrows the box where no rule does, which is how a
-            // widget with a natural pixel size -- an image, a gap -- gets that
-            // size rather than the whole offer. That is the offer's business
-            // rather than a declaration's, and this falls away once a widget
-            // occupies its reported size inside the box it was offered.
-            widget
-                .and_then(|widget| widget.size_hint(axis))
-                .filter(|len| len.leftover == Weight::ZERO)
+impl Widgets {
+    /// What a widget declares a length of its box to be. `leftover` is not
+    /// one: a share of what is left over is only a length to the widget
+    /// dividing one, so it passes up in the size instead.
+    pub(crate) fn declared_lens(&self, id: WidgetId) -> [Option<LayoutLen>; 2] {
+        let rules = self.size_rules(id);
+        let widget = self.get_dyn(id);
+        AXES.map(|axis| {
+            rules[axis].declared().or_else(|| {
+                // A hint still narrows the box where no rule does, which is
+                // how a widget with a natural pixel size -- an image, a gap
+                // -- gets that size rather than the whole offer. That is the
+                // offer's business rather than a declaration's, and this
+                // falls away once a widget occupies its reported size inside
+                // the box it was offered.
+                widget
+                    .and_then(|widget| widget.size_hint(axis))
+                    .filter(|len| len.leftover == Weight::ZERO)
+            })
         })
-    })
+    }
 }
 
-/// Whether what a widget reported along an axis is the whole of the box it
-/// is in rather than a part to be placed inside it. A share fills, because a
-/// share is a length only to whoever divides one, and whoever did is the one
-/// that handed down this box. A declared axis does too: the rule already gave
-/// the region its length, and the rule's length is what the widget reports
-/// there. And an axis the parent decided from the answer is
-/// the answer already.
-pub(crate) fn fills(reported: LayoutLen, declared: Option<LayoutLen>, decided: bool) -> bool {
-    reported.leftover != Weight::ZERO || declared.is_some() || decided
+impl LayoutLen {
+    /// Whether what a widget reported along an axis is the whole of the box
+    /// it is in rather than a part to be placed inside it. A share fills,
+    /// because a share is a length only to whoever divides one, and whoever
+    /// did is the one that handed down this box. A declared axis does too:
+    /// the rule already gave the region its length, and the rule's length is
+    /// what the widget reports there. And an axis the parent decided from
+    /// the answer is the answer already.
+    pub(crate) fn fills(self, declared: Option<LayoutLen>, decided: bool) -> bool {
+        self.leftover != Weight::ZERO || declared.is_some() || decided
+    }
 }
 
 /// Where a widget's drawing goes inside the part its parent gave it: what
@@ -685,63 +688,59 @@ pub(crate) fn fills(reported: LayoutLen, declared: Option<LayoutLen>, decided: b
 /// That is what makes a fraction the same fraction wherever the part it is
 /// placed in sits and however long it is -- the fraction is resolved once,
 /// here, against the rel base it was reported of.
-pub(crate) fn placement(
-    region: UiRegion,
-    size: Size,
-    declared: [Option<LayoutLen>; 2],
-    place: PlaceDesc,
-    align: RegionAlign,
-) -> UiRegion {
-    let mut placed = region;
-    for axis in AXES {
-        let n = axis as usize;
-        let reported = size.axis(axis);
-        if fills(reported, declared[n], place.axis(axis).does_fill()) {
-            continue;
+impl PlaceDesc {
+    pub(crate) fn placement(
+        self,
+        region: UiRegion,
+        size: Size,
+        declared: [Option<LayoutLen>; 2],
+        align: RegionAlign,
+    ) -> UiRegion {
+        let mut placed = region;
+        for axis in AXES {
+            let n = axis as usize;
+            let reported = size[axis];
+            if reported.fills(declared[n], self[axis].does_fill()) {
+                continue;
+            }
+            placed[axis] = placed[axis].place(reported.without_leftover(), align[axis]);
         }
-        let len = Len::from_parts(reported.rel, reported.px);
-        let span = placed.axis_mut(axis);
-        span.start += (span.len() - len).scale(align.axis(axis).rel());
-        span.end = span.start + len;
+        placed
     }
-    placed
-}
 
-/// The rel base length and the box a child is asked in, in the coordinates the
-/// widget asking draws in.
-///
-/// `own` is that widget's own box, and `place` what of it the child is
-/// given, including any rel base it states -- a row's slot, or padding's rel
-/// base less its pixels. That is a window length, like every other length
-/// here, since a slot of a row is not a fraction of anything the row can
-/// name. The child's declaration is a fraction of whichever reached it, and
-/// is the only one that also places the box: a box the caller decided is
-/// what `place` names.
-pub(crate) fn rel_base_and_region(
-    own: UiRegion,
-    parent_rel_base: UiVec2,
-    place: PlaceDesc,
-    declared: [Option<LayoutLen>; 2],
-    align: RegionAlign,
-) -> (UiVec2, UiRegion) {
-    let given = place.of(own, align);
-    let mut rel_base = parent_rel_base;
-    let mut region = given;
-    for axis in AXES {
-        let n = axis as usize;
-        let base = place
-            .axis(axis)
-            .stated_rel_base()
-            .unwrap_or_else(|| parent_rel_base.axis(axis));
-        let len = declared[n]
-            .map(|len| Len::from_parts(len.rel, len.px).within_len(base))
-            .unwrap_or(base);
-        *rel_base.axis_mut(axis) = len;
-        if declared[n].is_some() {
-            let slot = given.axis(axis);
-            let start = slot.start + (slot.len() - len).scale(align.axis(axis).rel());
-            *region.axis_mut(axis) = UiSpan::new(start, start + len);
+    /// The rel base length and the box a child is asked in, in the coordinates the
+    /// widget asking draws in.
+    ///
+    /// `own` is that widget's own box, and `place` what of it the child is
+    /// given, including any rel base it states -- a row's slot, or padding's rel
+    /// base less its pixels. That is a window length, like every other length
+    /// here, since a slot of a row is not a fraction of anything the row can
+    /// name. The child's declaration is a fraction of whichever reached it, and
+    /// is the only one that also places the box: a box the caller decided is
+    /// what `place` names.
+    pub(crate) fn rel_base_and_region(
+        self,
+        own: UiRegion,
+        parent_rel_base: UiVec2,
+        declared: [Option<LayoutLen>; 2],
+        align: RegionAlign,
+    ) -> (UiVec2, UiRegion) {
+        let given = self.of(own, align);
+        let mut rel_base = parent_rel_base;
+        let mut region = given;
+        for axis in AXES {
+            let n = axis as usize;
+            let base = self[axis]
+                .stated_rel_base()
+                .unwrap_or_else(|| parent_rel_base[axis]);
+            let len = declared[n]
+                .map(|len| len.without_leftover().within_len(base))
+                .unwrap_or(base);
+            rel_base[axis] = len;
+            if declared[n].is_some() {
+                region[axis] = given[axis].place(len, align[axis]);
+            }
         }
+        (rel_base, region)
     }
-    (rel_base, region)
 }
diff --git a/core/src/ui/place.rs b/core/src/ui/place.rs
index 7e61d7b..19ffae6 100644
--- a/core/src/ui/place.rs
+++ b/core/src/ui/place.rs
@@ -1,3 +1,4 @@
+use crate::util::impl_axis_index;
 use crate::{Axis, AxisAlign, Len, PrimitiveHandle, RegionAlign, UiRegion, UiSpan};
 
 /// How a child's region along one axis comes from the region of the widget
@@ -35,53 +36,7 @@ enum RelBase {
 
 impl PlaceDescAxis {
     /// The whole of the caller's box.
-    pub const WHOLE: Self = Self::within(UiSpan::FULL);
-
-    /// `span` composed into the caller's own box, so it moves and scales
-    /// with it: [`UiSpan::within`], which is what a container that insets
-    /// one speaks. Taking eleven pixels off the end needs no length, where
-    /// saying the same thing in window lengths would make the container read
-    /// its own box -- and a box chosen from its own answer then feeds back
-    /// into the answer.
-    ///
-    /// The child's rel base is narrowed the same way, so padding takes its
-    /// pixels off both and `rel(1)` under it fills the caller rather than
-    /// overflowing it.
-    pub const fn within(span: UiSpan) -> Self {
-        Self {
-            span: PlaceSpan::Within(span),
-            fills: false,
-            rel_base: RelBase::WithRegion,
-        }
-    }
-
-    /// `span` shifted to where the caller's own box starts: window lengths
-    /// along a cursor, which is what a container dividing room among its
-    /// children speaks. A child's report is a window length, so the cursor
-    /// that sums those reports is one too, and a moved box re-places every
-    /// child by re-adding its start, exactly.
-    ///
-    /// The child's rel base passes through: how far along the cursor a child
-    /// sits says nothing about what a fraction under it is of.
-    pub const fn shifted(span: UiSpan) -> Self {
-        Self {
-            span: PlaceSpan::Shifted(span),
-            fills: false,
-            rel_base: RelBase::Inherit,
-        }
-    }
-
-    /// A box this long, placed in the caller's own by the child's alignment:
-    /// the rule that places an answer, with the length given from above
-    /// rather than reported. What a stack's sizing child decides for the
-    /// rest. It is the child's rel base too.
-    pub const fn sized(len: Len) -> Self {
-        Self {
-            span: PlaceSpan::Sized(len),
-            fills: false,
-            rel_base: RelBase::Len(len),
-        }
-    }
+    pub const WHOLE: Self = UiSpan::FULL.within_desc();
 
     /// This region is the child's placement: its answer is not placed inside
     /// it again. A container uses it where it hands back exactly what the
@@ -91,6 +46,14 @@ impl PlaceDescAxis {
         self
     }
 
+    /// This along `axis`, and the whole of the caller's box across it: what
+    /// a container dividing one axis says, since nothing divides the other.
+    /// [`PlaceDesc::from_axis`] says the across one where it is not the
+    /// whole.
+    pub const fn axis(self, axis: Axis) -> PlaceDesc {
+        PlaceDesc::from_axis(axis, self, Self::WHOLE)
+    }
+
     /// What the child's fractions are of, as a length of the window: a
     /// resolved share, or a box a sibling's answer decided.
     pub const fn rel_base(mut self, len: Len) -> Self {
@@ -112,10 +75,7 @@ impl PlaceDescAxis {
                 span.shift(own.start);
                 span
             }
-            PlaceSpan::Sized(len) => {
-                let start = own.start + (own.len() - len).scale(align.rel());
-                UiSpan::new(start, start + len)
-            }
+            PlaceSpan::Sized(len) => own.place(len, align),
         }
     }
 
@@ -185,29 +145,21 @@ impl PlaceDesc {
         Self { x: place, y: place }
     }
 
+    /// A description per axis, where the two differ and neither is the
+    /// axis a container divides.
+    pub fn per_axis(f: impl Fn(Axis) -> PlaceDescAxis) -> Self {
+        Self::new(f(Axis::X), f(Axis::Y))
+    }
+
     /// `aligned` on `axis` and `ortho` on the other, which is how a
     /// container that divides one axis says what it is doing.
-    pub fn from_axis(axis: Axis, aligned: PlaceDescAxis, ortho: PlaceDescAxis) -> Self {
+    pub const fn from_axis(axis: Axis, aligned: PlaceDescAxis, ortho: PlaceDescAxis) -> Self {
         match axis {
             Axis::X => Self::new(aligned, ortho),
             Axis::Y => Self::new(ortho, aligned),
         }
     }
 
-    pub const fn axis(&self, axis: Axis) -> &PlaceDescAxis {
-        match axis {
-            Axis::X => &self.x,
-            Axis::Y => &self.y,
-        }
-    }
-
-    pub const fn axis_mut(&mut self, axis: Axis) -> &mut PlaceDescAxis {
-        match axis {
-            Axis::X => &mut self.x,
-            Axis::Y => &mut self.y,
-        }
-    }
-
     /// Both regions are the child's placement. See [`PlaceDescAxis::fills`].
     pub const fn fills(self) -> Self {
         Self::new(self.x.fills(), self.y.fills())
@@ -215,7 +167,7 @@ impl PlaceDesc {
 
     /// The child's rel base on one axis. See [`PlaceDescAxis::rel_base`].
     pub const fn rel_base(mut self, axis: Axis, len: Len) -> Self {
-        *self.axis_mut(axis) = self.axis(axis).rel_base(len);
+        self[axis] = self[axis].rel_base(len);
         self
     }
 
@@ -225,12 +177,61 @@ impl PlaceDesc {
     }
 }
 
+impl UiSpan {
+    /// This span composed into the caller's own box, so it moves and scales
+    /// with it: [`UiSpan::within`], which is what a container that insets
+    /// one speaks. Taking eleven pixels off the end needs no length, where
+    /// saying the same thing in window lengths would make the container read
+    /// its own box -- and a box chosen from its own answer then feeds back
+    /// into the answer.
+    ///
+    /// The child's rel base is narrowed the same way, so padding takes its
+    /// pixels off both and `rel(1)` under it fills the caller rather than
+    /// overflowing it.
+    pub const fn within_desc(self) -> PlaceDescAxis {
+        PlaceDescAxis {
+            span: PlaceSpan::Within(self),
+            fills: false,
+            rel_base: RelBase::WithRegion,
+        }
+    }
+
+    /// This span shifted to where the caller's own box starts: window
+    /// lengths along a cursor, which is what a container dividing room among
+    /// its children speaks. A child's report is a window length, so the
+    /// cursor that sums those reports is one too, and a moved box re-places
+    /// every child by re-adding its start, exactly.
+    ///
+    /// The child's rel base passes through: how far along the cursor a child
+    /// sits says nothing about what a fraction under it is of. The same span
+    /// says [`Self::within_desc`] as a part of that box instead, and which is
+    /// meant cannot be read off the numbers.
+    pub const fn shifted_desc(self) -> PlaceDescAxis {
+        PlaceDescAxis {
+            span: PlaceSpan::Shifted(self),
+            fills: false,
+            rel_base: RelBase::Inherit,
+        }
+    }
+}
+
+impl Len {
+    /// A box this long, placed in the caller's own by the child's alignment:
+    /// the rule that places an answer, with the length given from above
+    /// rather than reported. What a stack's sizing child decides for the
+    /// rest. It is the child's rel base too.
+    pub const fn as_desc(self) -> PlaceDescAxis {
+        PlaceDescAxis {
+            span: PlaceSpan::Sized(self),
+            fills: false,
+            rel_base: RelBase::Len(self),
+        }
+    }
+}
+
 impl From<UiRegion> for PlaceDesc {
     fn from(region: UiRegion) -> Self {
-        Self::new(
-            PlaceDescAxis::within(region.x),
-            PlaceDescAxis::within(region.y),
-        )
+        Self::new(region.x.within_desc(), region.y.within_desc())
     }
 }
 
@@ -247,3 +248,5 @@ pub struct RetainedPrimitive {
     pub handle: PrimitiveHandle,
     pub region: UiRegion,
 }
+
+impl_axis_index!(PlaceDesc => PlaceDescAxis);
diff --git a/core/src/ui/render_state.rs b/core/src/ui/render_state.rs
index 9c2160f..031431d 100644
--- a/core/src/ui/render_state.rs
+++ b/core/src/ui/render_state.rs
@@ -1,6 +1,5 @@
 #[cfg(feature = "layout-diagnostics")]
 use crate::layout_diagnostics::{self as diag, Counter, ReuseOutcome, TimerKind};
-use crate::ui::painter::{declared_lens, placement, rel_base_and_region};
 use crate::{
     ActiveData, Axis, DrawLayers, IdLike, LayoutHolds, LayoutLen, Len, MaskIdx, MoveIdx, Moves,
     Painter, PixelRegion, PlaceDesc, PxVec2, Rel, Size, StrongWidget, UiRegion, UiRsc, UiSpan,
@@ -194,11 +193,10 @@ impl UiRenderState {
     /// rules. Nothing above it narrowed anything or chose where it goes, so
     /// its declaration is the whole of what decides either.
     fn root_layout(id: WidgetId, widgets: &Widgets) -> (UiVec2, UiRegion) {
-        rel_base_and_region(
+        PlaceDesc::WHOLE.rel_base_and_region(
             UiRegion::FULL,
             UiVec2::FULL_SIZE,
-            PlaceDesc::WHOLE,
-            declared_lens(widgets, id),
+            widgets.declared_lens(id),
             widgets.alignment(id),
         )
     }
@@ -221,7 +219,7 @@ impl UiRenderState {
             diag::draw_request(id, info.parent, region, info.px, info.region_node);
         }
         let align = rsc.widgets().alignment(id);
-        let declared = declared_lens(rsc.widgets(), id);
+        let declared = rsc.widgets().declared_lens(id);
         // Nothing this widget measured can be dirty while it draws: layout is
         // one bottom-up walk, so anything deeper has settled or deferred to
         // its own parent, and a deferred one leaves that parent marked.
@@ -235,7 +233,7 @@ impl UiRenderState {
             .then(|| self.retained_answer(id, region, info))
             .flatten()
             .and_then(|answer| {
-                let placed = placement(region, answer.0, declared, info.placed, align);
+                let placed = info.placed.placement(region, answer.0, declared, align);
                 self.try_reuse(id, region, placed, info, rsc)
                     .map(|()| answer)
             });
@@ -247,7 +245,7 @@ impl UiRenderState {
             // Where the drawing goes: the part its parent gave it, with the
             // answer placed inside that part on any axis the parent left
             // open.
-            let placed = placement(region, answer.0, declared, info.placed, align);
+            let placed = info.placed.placement(region, answer.0, declared, align);
             if placed != region {
                 self.relocate(id, placed, info, rsc);
             }
@@ -292,8 +290,8 @@ impl UiRenderState {
             // A node entry is only a translation. Its local box keeps the
             // same window-unit length as the box in its parent's node.
             true => (
-                self.move_slot(id, info.parent_move, translation(region)),
-                local_region(region),
+                self.move_slot(id, info.parent_move, region.as_translation()),
+                region.at_origin(),
                 None,
             ),
             // Keep the old entry alive until every descendant has migrated.
@@ -377,14 +375,14 @@ impl UiRenderState {
         // resolved into the rel base when the child was asked, and resolving it
         // again here would take the fraction of a fraction.
         let rules = rsc.widgets().size_rules(id);
-        let ruled = |axis: Axis, reported: LayoutLen| match rules.axis(axis).exact() {
+        let ruled = |axis: Axis, reported: LayoutLen| match rules[axis].exact() {
             None => reported,
             Some(len) if len.leftover == Weight::ZERO => LayoutLen {
-                rel: info.rel_base.axis(axis).rel,
-                px: info.rel_base.axis(axis).px,
+                rel: info.rel_base[axis].rel,
+                px: info.rel_base[axis].px,
                 leftover: Weight::ZERO,
             },
-            Some(len) => len.within_len(info.rel_base.axis(axis)),
+            Some(len) => len.within_len(info.rel_base[axis]),
         };
         let size = Size {
             x: ruled(Axis::X, size.x),
@@ -399,7 +397,7 @@ impl UiRenderState {
             mask == info.mask
                 || AXES
                     .into_iter()
-                    .all(|axis| within_box(size, region, self.output_size, axis)),
+                    .all(|axis| size.within_box(region, self.output_size, axis)),
             "'{}' ({id:?}) clips to {px:?} and reports {size}",
             rsc.widgets().label(id),
         );
@@ -418,17 +416,13 @@ impl UiRenderState {
         // rel base's own length, so the answer is that rel base's and not just
         // that many pixels of this window -- the same pin a widget that read
         // its rel base took for its drawing.
-        let rel_base = AXES.map(|axis| {
-            let fraction = rules
-                .axis(axis)
-                .exact()
-                .is_some_and(|len| len.rel != Rel::ZERO);
-            match fraction {
-                true => Some(info.rel_base.axis(axis)),
-                false => own.rel_base[axis as usize],
+        let mut own_holds = own;
+        for axis in AXES {
+            let fraction = rules[axis].exact().is_some_and(|len| len.rel != Rel::ZERO);
+            if fraction {
+                own_holds[axis].rel_base = Some(info.rel_base[axis]);
             }
-        });
-        let own_holds = LayoutHolds { rel_base, ..own };
+        }
         let answer_holds = own_holds.and(answer_under);
         let holds = under
             .into_iter()
@@ -485,7 +479,7 @@ impl UiRenderState {
             mask_region,
             children,
             size_deps,
-            declared: declared_lens(rsc.widgets(), id),
+            declared: rsc.widgets().declared_lens(id),
             own_align: rsc.widgets().alignment(id),
             move_idx,
             parent_move: info.parent_move,
@@ -613,21 +607,21 @@ impl UiRenderState {
                 // Which of the three said no, so a rel base that redraws more
                 // than it should says where to look. They overlap: a drawing
                 // can be outside two of them at once.
-                let holds = active.holds;
                 for axis in AXES {
-                    let n = axis as usize;
-                    if holds.region_len[n].is_some_and(|pinned| pinned != region.axis(axis).len()) {
+                    let holds = active.holds[axis];
+                    let len = region[axis].len();
+                    let window = self.output_size[axis];
+                    if holds.region_len.is_some_and(|pinned| pinned != len) {
                         diag::bump(Counter::OutsidePinnedLen);
                     }
-                    if !holds.window[n].contains(self.output_size.axis(axis))
-                        || holds.rel_base[n]
-                            .is_some_and(|pinned| pinned != info.rel_base.axis(axis))
+                    if !holds.window.contains(window)
+                        || holds
+                            .rel_base
+                            .is_some_and(|pinned| pinned != info.rel_base[axis])
                     {
                         diag::bump(Counter::OutsideRelBase);
                     }
-                    if !holds.region[n]
-                        .contains(region.axis(axis).len().to_px(self.output_size.axis(axis)))
-                    {
+                    if !holds.region.contains(len.to_px(window)) {
                         diag::bump(Counter::OutsideRegion);
                     }
                 }
@@ -652,13 +646,13 @@ impl UiRenderState {
         );
         let has_region_node = active.move_idx != active.parent_move;
         let local = match has_region_node {
-            true => local_region(placed),
+            true => placed.at_origin(),
             false => placed,
         };
         let moved = active.placement != local;
         let slot = active.move_idx;
         if has_region_node {
-            self.moves.set(slot, translation(placed));
+            self.moves.set(slot, placed.as_translation());
         }
         if moved {
             self.reposition(id, local, info, rsc);
@@ -707,11 +701,10 @@ impl UiRenderState {
     ) {
         let active = &self.active[&child];
         let (rel_base, region) = Self::ask_again(active, at, place);
-        let placed = placement(
+        let placed = place.placement(
             region,
             active.measured().unwrap_or(active.size),
             active.declared,
-            place,
             active.own_align,
         );
         let info = DrawInfo {
@@ -736,13 +729,7 @@ impl UiRenderState {
     /// it declared are its own record's, so both are resolved against that
     /// parent's rel base again exactly as the first ask resolved them.
     fn ask_again(active: &ActiveData, at: &Placing, place: PlaceDesc) -> (UiVec2, UiRegion) {
-        rel_base_and_region(
-            at.region,
-            at.rel_base,
-            place,
-            active.declared,
-            active.own_align,
-        )
+        place.rel_base_and_region(at.region, at.rel_base, active.declared, active.own_align)
     }
 
     /// Re-places everything inside a widget whose own box moved. Every child
@@ -797,11 +784,8 @@ impl UiRenderState {
         let Some(widget) = rsc.widgets().get_dyn(id) else {
             return true;
         };
-        AXES.into_iter().all(|axis| {
-            widget
-                .size_hint(axis)
-                .is_none_or(|hint| hint == size.axis(axis))
-        })
+        AXES.into_iter()
+            .all(|axis| widget.size_hint(axis).is_none_or(|hint| hint == size[axis]))
     }
 
     /// Takes a widget's record out and frees what it drew.
@@ -1074,7 +1058,7 @@ impl UiRenderState {
         // to draw -- with the mark left on, so the parent draws it rather
         // than keeping it. So is a widget the parent asked twice: its
         // layout rests on an answer this widget cannot give again alone.
-        let declared_changed = declared_lens(rsc.widgets(), id) != active.declared;
+        let declared_changed = rsc.widgets().declared_lens(id) != active.declared;
         let alignment_changed = rsc.widgets().alignment(id) != active.own_align;
         if let Some(parent) = active.parent
             && (declared_changed
@@ -1189,29 +1173,33 @@ impl UiRenderState {
 /// Both are lengths of the window, so the comparison is in its pixels. A
 /// share is a length only to whoever divides one, so it is not a claim about
 /// this box and cannot exceed it.
-fn within_box(size: Size, region: UiRegion, window: PxVec2, axis: Axis) -> bool {
-    let len = size.axis(axis);
-    let window = window.axis(axis);
-    len.leftover != Weight::ZERO
-        || Len::from_parts(len.rel, len.px).to_px(window) <= region.axis(axis).len().to_px(window)
+impl Size {
+    fn within_box(self, region: UiRegion, window: PxVec2, axis: Axis) -> bool {
+        let len = self[axis];
+        let window = window[axis];
+        len.leftover != Weight::ZERO
+            || len.without_leftover().to_px(window) <= region[axis].len().to_px(window)
+    }
 }
 
-/// A box in a fresh region node keeps its window-unit length and starts at
-/// that node's origin.
-fn local_region(region: UiRegion) -> UiRegion {
-    let size = region.size();
-    UiRegion::new(
-        UiSpan::new(Len::ZERO, size.x),
-        UiSpan::new(Len::ZERO, size.y),
-    )
-}
+impl UiRegion {
+    /// A box in a fresh region node keeps its window-unit length and starts
+    /// at that node's origin.
+    fn at_origin(self) -> UiRegion {
+        let size = self.size();
+        UiRegion::new(
+            UiSpan::new(Len::ZERO, size.x),
+            UiSpan::new(Len::ZERO, size.y),
+        )
+    }
 
-/// A region node changes only the origin. A full relative span anchored at
-/// the box start composes as that translation in both the CPU and shader.
-fn translation(region: UiRegion) -> UiRegion {
-    UiRegion {
-        x: UiSpan::new(region.x.start, region.x.start + Len::FULL),
-        y: UiSpan::new(region.y.start, region.y.start + Len::FULL),
+    /// A region node changes only the origin. A full relative span anchored at
+    /// the box start composes as that translation in both the CPU and shader.
+    fn as_translation(self) -> UiRegion {
+        UiRegion {
+            x: UiSpan::new(self.x.start, self.x.start + Len::FULL),
+            y: UiSpan::new(self.y.start, self.y.start + Len::FULL),
+        }
     }
 }
 
diff --git a/core/src/util/math.rs b/core/src/util/math.rs
index 95e7eef..cf251c1 100644
--- a/core/src/util/math.rs
+++ b/core/src/util/math.rs
@@ -93,3 +93,31 @@ macro_rules! impl_op {
 }
 
 pub(crate) use impl_op;
+
+/// `Index<Axis>` for a pair, which is how every pair here is read by axis.
+/// The generics clause is given in braces where the type has one.
+macro_rules! impl_axis_index {
+    ($({$($gen:tt)*})? $T:ty => $Out:ty) => {
+        const impl $(<$($gen)*>)? std::ops::Index<crate::Axis> for $T {
+            type Output = $Out;
+
+            fn index(&self, axis: crate::Axis) -> &$Out {
+                match axis {
+                    crate::Axis::X => &self.x,
+                    crate::Axis::Y => &self.y,
+                }
+            }
+        }
+
+        const impl $(<$($gen)*>)? std::ops::IndexMut<crate::Axis> for $T {
+            fn index_mut(&mut self, axis: crate::Axis) -> &mut $Out {
+                match axis {
+                    crate::Axis::X => &mut self.x,
+                    crate::Axis::Y => &mut self.y,
+                }
+            }
+        }
+    };
+}
+
+pub(crate) use impl_axis_index;
diff --git a/core/src/widget/size_rule.rs b/core/src/widget/size_rule.rs
index d046ed4..d3a0f5e 100644
--- a/core/src/widget/size_rule.rs
+++ b/core/src/widget/size_rule.rs
@@ -1,4 +1,5 @@
-use crate::{Axis, LayoutLen, Weight};
+use crate::util::impl_axis_index;
+use crate::{LayoutLen, Weight};
 
 /// What a widget's length on one axis is, as a rule its parent applies where
 /// it draws it rather than an answer the widget gives about itself.
@@ -70,18 +71,4 @@ pub struct SizeRules {
     pub y: SizeRule,
 }
 
-impl SizeRules {
-    pub fn axis(&self, axis: Axis) -> SizeRule {
-        match axis {
-            Axis::X => self.x,
-            Axis::Y => self.y,
-        }
-    }
-
-    pub fn axis_mut(&mut self, axis: Axis) -> &mut SizeRule {
-        match axis {
-            Axis::X => &mut self.x,
-            Axis::Y => &mut self.y,
-        }
-    }
-}
+impl_axis_index!(SizeRules => SizeRule);
diff --git a/core/src/widget/widgets.rs b/core/src/widget/widgets.rs
index 6856d24..3dc044d 100644
--- a/core/src/widget/widgets.rs
+++ b/core/src/widget/widgets.rs
@@ -130,10 +130,10 @@ impl Widgets {
     pub fn set_size_rule(&mut self, id: impl IdLike, axis: Axis, rule: SizeRule) {
         let id = id.id();
         let data = self.data_mut(id).unwrap();
-        if *data.size.axis_mut(axis) == rule {
+        if data.size[axis] == rule {
             return;
         }
-        *data.size.axis_mut(axis) = rule;
+        data.size[axis] = rule;
         self.needs_redraw.insert(id);
     }
 
@@ -147,10 +147,10 @@ impl Widgets {
     pub fn set_alignment(&mut self, id: impl IdLike, axis: Axis, align: AxisAlign) {
         let id = id.id();
         let data = self.data_mut(id).unwrap();
-        if *data.align.axis_mut(axis) == align {
+        if data.align[axis] == align {
             return;
         }
-        *data.align.axis_mut(axis) = align;
+        data.align[axis] = align;
         self.needs_redraw.insert(id);
     }
 
diff --git a/src/random.rs b/src/random.rs
index 5c49e30..6bf939c 100644
--- a/src/random.rs
+++ b/src/random.rs
@@ -118,9 +118,9 @@ pub struct Branch {
 impl Widget for Branch {
     fn draw(&mut self, painter: &mut Painter) -> Size {
         let cut = Len::from_parts(Rel::ZERO, Px::from_int(40));
-        let top = PlaceDescAxis::shifted(UiSpan::new(Len::ZERO, cut));
+        let top = UiSpan::new(Len::ZERO, cut).shifted_desc();
         let measured = painter
-            .widget_at(&self.probe, PlaceDesc::new(PlaceDescAxis::WHOLE, top))
+            .widget_at(&self.probe, top.axis(Axis::Y))
             .len(Axis::X);
         let len = measured.apply_leftover();
         let px = painter.to_px(len, Axis::X);
@@ -134,8 +134,8 @@ impl Widget for Branch {
         };
         painter.window_holds(Axis::X, holds.through(len));
 
-        let below = PlaceDescAxis::shifted(UiSpan::new(cut, painter.region_len(Axis::Y)));
-        let place = PlaceDesc::new(PlaceDescAxis::WHOLE, below);
+        let below = UiSpan::new(cut, painter.region_len(Axis::Y)).shifted_desc();
+        let place = below.axis(Axis::Y);
         match px > threshold {
             true => painter.widget_at(&self.wide, place),
             false => painter.widget_at(&self.narrow, place),
diff --git a/src/widget/image.rs b/src/widget/image.rs
index c6bb62e..50bd1ff 100644
--- a/src/widget/image.rs
+++ b/src/widget/image.rs
@@ -12,7 +12,7 @@ impl Widget for Image {
     }
 
     fn size_hint(&self, axis: Axis) -> Option<LayoutLen> {
-        Some(LayoutLen::px(self.handle.size().axis(axis)))
+        Some(LayoutLen::px(self.handle.size()[axis]))
     }
 }
 
diff --git a/src/widget/position/scroll.rs b/src/widget/position/scroll.rs
index ab369b0..7e66cc8 100644
--- a/src/widget/position/scroll.rs
+++ b/src/widget/position/scroll.rs
@@ -16,7 +16,7 @@ impl Widget for Scroll {
         let answer_len = painter
             .widget_at(&self.inner, PlaceDesc::WHOLE.fills())
             .len(self.axis);
-        let fixed = painter.to_px(Len::from_parts(answer_len.rel, answer_len.px), self.axis);
+        let fixed = painter.to_px(answer_len.without_leftover(), self.axis);
         self.container_len = container_len;
         self.content_len = fixed.max(container_len);
 
@@ -24,14 +24,14 @@ impl Widget for Scroll {
             self.amt = self.content_len - self.container_len;
         }
         self.update_amt();
-        let align = painter.alignment().axis(self.axis);
+        let align = painter.alignment()[self.axis];
         // Content of a fixed length that fits sits at the start of any box it
         // fits in -- but only anchored there. Anywhere else it is a part of
         // the room left over, so it moves with every length the box takes and
         // the drawing holds for that length alone. One scrolled part way sits
         // where it is until the box shrinks past what is left of it. Kept to
         // the end, it moves with every length.
-        let fixed_len = answer_len.rel == Rel::ZERO && answer_len.leftover == Weight::ZERO;
+        let fixed_len = answer_len.is_px();
         if fixed_len && self.content_len <= self.container_len && align == AxisAlign::NEG {
             painter.holds(self.axis, fixed..=Px::MAX);
         } else if fixed_len && !self.snap_end {
@@ -54,7 +54,7 @@ impl Widget for Scroll {
         let content = match moved || self.content_len != self.container_len {
             true => {
                 let start = Len::from_parts(Rel::ZERO, anchor - self.amt);
-                PlaceDescAxis::shifted(UiSpan::new(start, start.offset(self.content_len)))
+                UiSpan::new(start, start.offset(self.content_len)).shifted_desc()
             }
             false => PlaceDescAxis::WHOLE,
         };
@@ -62,10 +62,7 @@ impl Widget for Scroll {
         // reports is a fraction of what is on screen rather than of the
         // content box its own answer decided. Where it goes is the content
         // box, scrolled: its drawing moved there, not made again there.
-        painter.place_at(
-            &self.inner,
-            PlaceDesc::from_axis(self.axis, content.fills(), PlaceDescAxis::WHOLE.fills()),
-        );
+        painter.place_at(&self.inner, content.axis(self.axis).fills());
         // What it occupies is its box, on both axes: it clips its content to
         // that box, so it can neither take less of one nor honestly ask for
         // more. The content's length is what it scrolls through, not what it
diff --git a/src/widget/position/span.rs b/src/widget/position/span.rs
index 435ccf2..b99ef0b 100644
--- a/src/widget/position/span.rs
+++ b/src/widget/position/span.rs
@@ -18,10 +18,6 @@ impl Widget for Span {
             Sign::Pos => UiSpan::new(from, to),
             Sign::Neg => UiSpan::new(far - to, far - from),
         };
-        // Across itself the child sits where its own alignment says, in the
-        // whole of the row: a span is what contains its children there, and
-        // nothing divides that axis.
-        let across = PlaceDescAxis::WHOLE;
         // A length for every child before their final slots are chosen: from
         // a hint where one says, and from drawing otherwise. The rel base passes
         // through unchanged, so `rel(0.5)` is half the area this span was
@@ -34,10 +30,11 @@ impl Widget for Span {
             let len = match painter.size_hint(child, axis) {
                 Some(len) => len,
                 None => {
-                    let room = PlaceDescAxis::shifted(along(cursor, far));
-                    painter
-                        .widget_at(child, PlaceDesc::from_axis(axis, room, across))
-                        .len(axis)
+                    // Across itself the child sits where its own alignment
+                    // says, in the whole of the row: a span is what contains
+                    // its children there, and nothing divides that axis.
+                    let room = along(cursor, far).shifted_desc().axis(axis);
+                    painter.widget_at(child, room).len(axis)
                 }
             };
             cursor.px += len.px + self.gap;
@@ -58,7 +55,7 @@ impl Widget for Span {
 
         // What is left for the shares to divide: the row less everything
         // fixed, as a length of the rel base rather than a number of pixels.
-        let room = far - Len::from_parts(total.rel, total.px);
+        let room = far - total.without_leftover();
         // Whether anything is left over is a question in pixels: `rel(0.5)`
         // beside 300 px is full at 600 and overfull at 400. Asked of `room`
         // itself, and answered back through the same expression, so the
@@ -94,24 +91,26 @@ impl Widget for Span {
         let mut taken = Weight::ZERO;
         let mut start = Len::rel_min();
         let mut ortho = LayoutLen::ZERO;
+        let shared = |fixed: Len, taken: Weight| match taken == Weight::ZERO {
+            true => fixed,
+            false => fixed + room.scale(Rel::ratio(taken, total.leftover)),
+        };
         for (child, &len) in self.children.iter().zip(&lens) {
             // A child asking for nothing but a part of what is left over,
             // when nothing is, is not drawn at all. One that also asked for
             // pixels or a fraction keeps those and overflows.
-            if len.leftover > Weight::ZERO && len.px == Px::ZERO && len.rel == Rel::ZERO && !shares
-            {
+            if len.is_only_leftover() && !shares {
                 painter.undraw(child);
                 fixed.px += self.gap;
-                start = shared(fixed, taken, total.leftover, room);
+                start = shared(fixed, taken);
                 continue;
             }
             let from = start;
             if len.leftover > Weight::ZERO && shares {
                 taken += len.leftover;
             }
-            fixed.px += len.px;
-            fixed.rel += len.rel;
-            start = shared(fixed, taken, total.leftover, room);
+            fixed += len.without_leftover();
+            start = shared(fixed, taken);
             // Along the row the span says where the child goes, and that slot
             // is the child's box outright rather than something to place an
             // answer inside again. A share is decided here and nowhere
@@ -120,8 +119,7 @@ impl Widget for Span {
             // fixed child's slot is its own answer, so a drawing made in the
             // room is put there as it is, and one not made yet is made here.
             let slot = along(from, start);
-            let slot_place = PlaceDescAxis::shifted(slot).fills();
-            let mut place = PlaceDesc::from_axis(axis, slot_place, across);
+            let mut place = slot.shifted_desc().fills().axis(axis);
             if len.leftover > Weight::ZERO && shares {
                 place = place.rel_base(axis, slot.len());
             }
@@ -131,14 +129,14 @@ impl Widget for Span {
                 // span's own eventual width admits multiple fixed points.
                 // A scalable child therefore makes Children scalable too;
                 // only fixed children are compared with one another.
-                if used.rel != Rel::ZERO || used.leftover != Weight::ZERO {
+                if !used.is_px() {
                     ortho = LayoutLen::LEFTOVER;
                 } else if ortho.leftover == Weight::ZERO {
                     ortho.px = ortho.px.max(used.px);
                 }
             }
             fixed.px += self.gap;
-            start = shared(fixed, taken, total.leftover, room);
+            start = shared(fixed, taken);
         }
 
         // Carried whole rather than collapsed to one share: a span that sizes
@@ -157,16 +155,6 @@ impl Widget for Span {
     }
 }
 
-/// Where a row has reached: everything fixed before this point, which is a
-/// sum and exact, plus the share of the room the weights so far are worth,
-/// which is one rounding wherever it is asked for.
-fn shared(fixed: Len, taken: Weight, weight: Weight, room: Len) -> Len {
-    if taken == Weight::ZERO {
-        return fixed;
-    }
-    fixed + room.scale(Rel::ratio(taken, weight))
-}
-
 impl Span {
     pub fn empty(dir: Dir) -> Self {
         Self {
diff --git a/src/widget/position/stack.rs b/src/widget/position/stack.rs
index 17d15ff..a5a6323 100644
--- a/src/widget/position/stack.rs
+++ b/src/widget/position/stack.rs
@@ -31,14 +31,13 @@ impl Widget for Stack {
         // fraction under them is a fraction of it. A share leaves the axis
         // to whoever gave the stack its box. Where a child sits in a box
         // bigger than itself is its own business.
-        let on = |axis| {
-            let len = size.axis(axis);
+        let place = PlaceDesc::per_axis(|axis| {
+            let len = size[axis];
             match len.leftover == Weight::ZERO {
-                true => PlaceDescAxis::sized(Len::from_parts(len.rel, len.px)).fills(),
+                true => len.without_leftover().as_desc().fills(),
                 false => PlaceDescAxis::WHOLE,
             }
-        };
-        let place = PlaceDesc::new(on(Axis::X), on(Axis::Y));
+        });
         for (i, child) in self.children.iter().enumerate() {
             if sizing == Some(i) {
                 continue;
diff --git a/tests/cases/determinism.rs b/tests/cases/determinism.rs
index 3c78c16..fd98eb3 100644
--- a/tests/cases/determinism.rs
+++ b/tests/cases/determinism.rs
@@ -22,14 +22,14 @@ struct BranchesOnMeasurement {
 impl Widget for BranchesOnMeasurement {
     fn draw(&mut self, painter: &mut Painter) -> Size {
         let cut = Len::from_parts(Rel::ZERO, Px::from_int(40));
-        let top = PlaceDescAxis::shifted(UiSpan::new(Len::ZERO, cut));
+        let top = UiSpan::new(Len::ZERO, cut).shifted_desc();
         let measured = painter
-            .widget_at(&self.probe, PlaceDesc::new(PlaceDescAxis::WHOLE, top))
+            .widget_at(&self.probe, top.axis(Axis::Y))
             .len(Axis::X);
         let px = painter.to_px(measured.apply_leftover(), Axis::X);
 
-        let below = PlaceDescAxis::shifted(UiSpan::new(cut, painter.region_len(Axis::Y)));
-        let place = PlaceDesc::new(PlaceDescAxis::WHOLE, below);
+        let below = UiSpan::new(cut, painter.region_len(Axis::Y)).shifted_desc();
+        let place = below.axis(Axis::Y);
         match px > Px::from_f32(self.threshold) {
             true => painter.widget_at(&self.wide, place),
             false => painter.widget_at(&self.narrow, place),
diff --git a/tests/cases/layout.rs b/tests/cases/layout.rs
index a62d857..2435775 100644
--- a/tests/cases/layout.rs
+++ b/tests/cases/layout.rs
@@ -501,10 +501,10 @@ fn a_row_of_equal_shares_fills_it_exactly() {
 fn drawn_edges(h: &Harness, id: WidgetId, axis: Axis) -> (f32, f32) {
     let active = &h.render.active[&id];
     let region = h.render.moves.resolve(active.move_idx, active.placement);
-    let dim = h.size().axis(axis);
+    let dim = h.size()[axis];
     let snap = |v: f32| (v + Px::STEP.to_f32() * 0.5).floor();
     let edge = |s: Len| snap(s.rel.to_f32() * dim + s.px.to_f32());
-    let span = region.axis(axis);
+    let span = region[axis];
     (edge(span.start), edge(span.end))
 }
 
@@ -853,8 +853,8 @@ fn a_collapsed_share_keeps_the_gaps_before_the_next_slot() {
                 Sign::Pos => (400 - tail_len, 400),
                 Sign::Neg => (0, tail_len),
             };
-            assert_eq!(region.top_left.axis(dir.axis), Px::from_int(from));
-            assert_eq!(region.bot_right.axis(dir.axis), Px::from_int(to));
+            assert_eq!(region.top_left[dir.axis], Px::from_int(from));
+            assert_eq!(region.bot_right[dir.axis], Px::from_int(to));
         }
     }
 }
diff --git a/tests/cases/retained.rs b/tests/cases/retained.rs
index a9254fc..c95f213 100644
--- a/tests/cases/retained.rs
+++ b/tests/cases/retained.rs
@@ -214,10 +214,7 @@ impl Widget for FromHint {
     fn draw(&mut self, painter: &mut Painter) -> Size {
         let len = painter.size_hint(&self.inner, Axis::Y).unwrap();
         let top = UiSpan::new(Len::ZERO, Len::from_parts(Rel::ZERO, len.px));
-        painter.widget_at(
-            &self.inner,
-            PlaceDesc::new(PlaceDescAxis::WHOLE, PlaceDescAxis::shifted(top)),
-        );
+        painter.widget_at(&self.inner, top.shifted_desc().axis(Axis::Y));
         Size::LEFTOVER
     }
 }
@@ -876,10 +873,7 @@ fn resizing_a_fixed_frame_recomposes_its_contents_without_drawing_them() {
         fn draw(&mut self, painter: &mut Painter) -> Size {
             painter.widget_at(
                 &self.child,
-                PlaceDesc::new(
-                    PlaceDescAxis::shifted(self.region.x),
-                    PlaceDescAxis::shifted(self.region.y),
-                ),
+                PlaceDesc::new(self.region.x.shifted_desc(), self.region.y.shifted_desc()),
             );
             Size::LEFTOVER
         }
@@ -965,8 +959,8 @@ fn glyph_origins_compose_identically_when_drawn_and_when_retained() {
             painter.widget_at(
                 &self.child,
                 PlaceDesc::new(
-                    PlaceDescAxis::shifted(self.region.x).fills(),
-                    PlaceDescAxis::shifted(self.region.y).fills(),
+                    self.region.x.shifted_desc().fills(),
+                    self.region.y.shifted_desc().fills(),
                 )
                 .rel_base(Axis::X, self.frame.x.len()),
             );
@@ -1135,8 +1129,8 @@ fn padding_and_stack_boxes_follow_the_region_without_drawing_again() {
             painter.widget_at(
                 &self.child,
                 PlaceDesc::new(
-                    PlaceDescAxis::shifted(self.region.x).fills(),
-                    PlaceDescAxis::shifted(self.region.y).fills(),
+                    self.region.x.shifted_desc().fills(),
+                    self.region.y.shifted_desc().fills(),
                 ),
             );
             Size::LEFTOVER
@@ -1222,12 +1216,10 @@ fn moving_a_childs_region_preserves_the_slot_chosen_from_its_measurement() {
             painter.widget_at(
                 &self.child,
                 PlaceDesc::new(
-                    PlaceDescAxis::shifted(UiSpan::new(
-                        Len::px(self.start),
-                        Len::px(self.start + 200.0),
-                    ))
-                    .fills(),
-                    PlaceDescAxis::shifted(UiSpan::FULL).fills(),
+                    UiSpan::new(Len::px(self.start), Len::px(self.start + 200.0))
+                        .shifted_desc()
+                        .fills(),
+                    UiSpan::FULL.shifted_desc().fills(),
                 ),
             );
             Size::LEFTOVER
@@ -1263,10 +1255,7 @@ fn changing_regions_keep_fractional_reports_and_numeric_dependencies_valid() {
             painter
                 .widget_at(
                     &self.child,
-                    PlaceDesc::new(
-                        PlaceDescAxis::shifted(self.region.x),
-                        PlaceDescAxis::shifted(self.region.y),
-                    ),
+                    PlaceDesc::new(self.region.x.shifted_desc(), self.region.y.shifted_desc()),
                 )
                 .size()
         }
@@ -1283,8 +1272,8 @@ fn changing_regions_keep_fractional_reports_and_numeric_dependencies_valid() {
                     .widget_at(
                         &self.child,
                         PlaceDesc::new(
-                            PlaceDescAxis::shifted(self.region.x).fills(),
-                            PlaceDescAxis::shifted(self.region.y).fills(),
+                            self.region.x.shifted_desc().fills(),
+                            self.region.y.shifted_desc().fills(),
                         ),
                     )
                     .size(),