diff --git a/core/src/orientation/pos.rs b/core/src/orientation/pos.rs
index 9d73394..e9afd75 100644
--- a/core/src/orientation/pos.rs
+++ b/core/src/orientation/pos.rs
@@ -28,6 +28,14 @@ impl UiVec2 {
         }
     }
 
+    /// From lengths already on the grid, with no fraction of a box.
+    pub const fn from_px(px: PxVec2) -> Self {
+        Self {
+            x: UiScalar::from_parts(Rel::ZERO, px.x),
+            y: UiScalar::from_parts(Rel::ZERO, px.y),
+        }
+    }
+
     pub const fn rel(rel: impl const Into<Vec2>) -> Self {
         let rel = rel.into();
         Self {
diff --git a/core/src/primitive/text.rs b/core/src/primitive/text.rs
index 941f123..1fa9f92 100644
--- a/core/src/primitive/text.rs
+++ b/core/src/primitive/text.rs
@@ -1,7 +1,8 @@
 #[cfg(feature = "layout-diagnostics")]
 use crate::layout_diagnostics::{self as diag, Counter, TimerKind};
 use crate::{
-    Align, GlyphAtlas, GlyphEntry, GlyphKey, PlacedGlyph, RegionAlign, UiColor, util::Vec2,
+    Align, GlyphAtlas, GlyphEntry, GlyphKey, PlacedGlyph, Px, PxVec2, RegionAlign, UiColor,
+    util::Vec2,
 };
 use parley::{
     Alignment, AlignmentOptions, FontContext, FontFamily, FontFamilyName, GenericFamily, Layout,
@@ -303,9 +304,9 @@ impl TextData {
                     };
                     placed.push(PlacedGlyph {
                         entry,
-                        offset: Vec2::new(
-                            glyph.x.floor() + entry.left as f32,
-                            glyph.y.floor() - entry.top as f32,
+                        offset: PxVec2::new(
+                            Px::from_int(glyph.x.floor() as i32 + entry.left),
+                            Px::from_int(glyph.y.floor() as i32 - entry.top),
                         ),
                     });
                 }
diff --git a/core/src/render/atlas.rs b/core/src/render/atlas.rs
index 2325f4a..170bdeb 100644
--- a/core/src/render/atlas.rs
+++ b/core/src/render/atlas.rs
@@ -1,5 +1,5 @@
 use crate::{
-    PatchRect,
+    PatchRect, PxVec2,
     util::{HashMap, Vec2},
 };
 use image::RgbaImage;
@@ -241,5 +241,7 @@ fn write_glyph(page: &mut RgbaImage, image: &Image, x: u32, y: u32) {
 #[derive(Clone, Copy)]
 pub struct PlacedGlyph {
     pub entry: GlyphEntry,
-    pub offset: Vec2,
+    /// Whole pixels from the origin of the text to this glyph's top-left,
+    /// on the grid once here rather than on every frame that draws it.
+    pub offset: PxVec2,
 }
diff --git a/core/src/ui/painter.rs b/core/src/ui/painter.rs
index 653c36c..9df8484 100644
--- a/core/src/ui/painter.rs
+++ b/core/src/ui/painter.rs
@@ -326,9 +326,13 @@ impl<'a> Painter<'a> {
             let mut region = origin;
             region.x.end = region.x.start;
             region.y.end = region.y.start;
-            let mut region = region.offset(UiVec2::px(glyph.offset));
-            region.x.end = region.x.start + UiScalar::px(glyph.entry.width as f32);
-            region.y.end = region.y.start + UiScalar::px(glyph.entry.height as f32);
+            let mut region = region.offset(UiVec2::from_px(glyph.offset));
+            let size = PxVec2::new(
+                Px::from_int(glyph.entry.width as i32),
+                Px::from_int(glyph.entry.height as i32),
+            );
+            region.x.end = region.x.start.offset(size.x);
+            region.y.end = region.y.start.offset(size.y);
             self.write(
                 kind,
                 GlyphPrimitive {