diff --git a/crates/gpu/src/fx.rs b/crates/gpu/src/fx.rs
index 972ccadbea..4f265a3202 100644
--- a/crates/gpu/src/fx.rs
+++ b/crates/gpu/src/fx.rs
@@ -336,8 +336,10 @@ fn bands(r: Rect, rows: i32) -> Vec<Rect> {
     let mut out = Vec::new();
     let mut y = r.y0;
     while y < r.y1 {
-        out.push(Rect::new(r.x0, y, r.x1, (y + rows).min(r.y1)));
-        y += rows;
+        // Saturating near the coordinate ceiling: a wrapped edge would never reach `y1`.
+        let end = y.saturating_add(rows.max(1)).min(r.y1);
+        out.push(Rect::new(r.x0, y, r.x1, end));
+        y = end;
     }
     out
 }
diff --git a/crates/gpu/src/fx/tests.rs b/crates/gpu/src/fx/tests.rs
index 1622da28e2..d796288eeb 100644
--- a/crates/gpu/src/fx/tests.rs
+++ b/crates/gpu/src/fx/tests.rs
@@ -308,3 +308,12 @@ fn shape_tiles_and_group_pins_hold_addresses_not_pixels() {
     drop(group);
     assert!(pins.iter().all(|w| w.strong_count() == 0), "a group's pins keep none of its pixels");
 }
+
+#[test]
+fn bands_end_at_the_coordinate_ceiling() {
+    let r = Rect::new(0, i32::MAX - 100, 8, i32::MAX);
+    let bands = super::bands(r, 64);
+    assert_eq!(bands.len(), 2, "{bands:?}");
+    assert_eq!((bands[0].y0, bands[0].y1, bands[1].y1), (i32::MAX - 100, i32::MAX - 36, i32::MAX));
+    assert_eq!(super::bands(Rect::new(0, 0, 8, 10), 0).len(), 10, "a zero step still makes progress");
+}