diff --git a/core/src/ui/render_state.rs b/core/src/ui/render_state.rs
index 4d169c2..b62d68b 100644
--- a/core/src/ui/render_state.rs
+++ b/core/src/ui/render_state.rs
@@ -69,6 +69,10 @@ pub struct UiRenderState {
     /// Widgets waiting for an ancestor to draw them, so the walk down the
     /// depths does not pick one up again at its own depth.
     deferred: crate::util::HashSet<WidgetId>,
+    /// What the walk has left to settle, deepest last. Ordered rather than
+    /// searched: the set is scanned once a frame, and every mark made while
+    /// the walk runs puts itself in place.
+    pending: std::collections::BTreeSet<(usize, WidgetId)>,
     pub moves: Moves,
 }
 
@@ -81,6 +85,7 @@ impl UiRenderState {
             old_root: None,
             slots: Default::default(),
             deferred: Default::default(),
+            pending: Default::default(),
             moves: Default::default(),
             resized: false,
         }
@@ -994,15 +999,25 @@ impl UiRenderState {
         // something below is about to change it -- which is the whole class
         // of defect where a widget settles inside its parent's draw, clears
         // its mark there, and tells nobody its answer moved.
-        loop {
-            let next = rsc
-                .widgets()
-                .needs_redraw
-                .iter()
-                .copied()
-                .filter(|id| !self.deferred.contains(id))
-                .max_by_key(|&id| self.depth(id));
-            let Some(id) = next else { break };
+        let marked: Vec<WidgetId> = rsc.widgets().needs_redraw.iter().copied().collect();
+        for id in marked {
+            let depth = self.depth(id);
+            self.pending.insert((depth, id));
+        }
+        while let Some(&(depth, id)) = self.pending.last() {
+            self.pending.remove(&(depth, id));
+            // A widget settled inside an ancestor's draw, or deferred to one,
+            // is left here by the mark that queued it.
+            if self.deferred.contains(&id) || !rsc.widgets().needs_redraw.contains(&id) {
+                continue;
+            }
+            // A subtree that changed hands takes its descendants' depths with
+            // it, so an entry queued before that move names the wrong one.
+            let now = self.depth(id);
+            if now != depth {
+                self.pending.insert((now, id));
+                continue;
+            }
             #[cfg(feature = "layout-diagnostics")]
             diag::bump(Counter::QueuePops);
             if !self.redraw(id, rsc) {
@@ -1012,6 +1027,16 @@ impl UiRenderState {
         self.deferred.clear();
     }
 
+    /// Marks a widget for the walk to settle. Every mark made while a frame
+    /// is being laid out goes through here, so the queue holds what the set
+    /// holds without being searched again.
+    fn mark(&mut self, id: WidgetId, widgets: &mut Widgets) {
+        if widgets.needs_redraw.insert(id) && !self.deferred.contains(&id) {
+            let depth = self.depth(id);
+            self.pending.insert((depth, id));
+        }
+    }
+
     fn depth(&self, id: WidgetId) -> usize {
         #[cfg(feature = "layout-diagnostics")]
         diag::bump(Counter::DepthReads);
@@ -1115,8 +1140,8 @@ impl UiRenderState {
             // Both stay marked: the parent because it has this to draw, and
             // this because the parent must draw it rather than keep what it
             // has. The mark comes off in `draw_at`, where the parent draws.
-            rsc.widgets_mut().needs_redraw.insert(id);
-            rsc.widgets_mut().needs_redraw.insert(parent);
+            self.mark(id, rsc.widgets_mut());
+            self.mark(parent, rsc.widgets_mut());
             return false;
         }
         if !active.drawn {
@@ -1144,8 +1169,8 @@ impl UiRenderState {
         // mark left on. Lengths and not whole boxes: what a drawing depends
         // on is its lengths, so the same lengths elsewhere is one question.
         if given_px != offered_px {
-            rsc.widgets_mut().needs_redraw.insert(id);
-            rsc.widgets_mut().needs_redraw.insert(parent);
+            self.mark(id, rsc.widgets_mut());
+            self.mark(parent, rsc.widgets_mut());
             return false;
         }
         let info = DrawInfo {
@@ -1200,7 +1225,7 @@ impl UiRenderState {
                 diag::bump(Counter::SizeChanges);
                 diag::bump(Counter::ReaderEdges);
             }
-            rsc.widgets_mut().needs_redraw.insert(parent);
+            self.mark(parent, rsc.widgets_mut());
         }
         true
     }
diff --git a/core/src/util/slot.rs b/core/src/util/slot.rs
index 94fd2a1..707b0bf 100644
--- a/core/src/util/slot.rs
+++ b/core/src/util/slot.rs
@@ -1,4 +1,4 @@
-#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash)]
+#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash, PartialOrd, Ord)]
 pub struct SlotId {
     idx: u32,
     genr: u32,