diff --git a/crates/compose/src/lib.rs b/crates/compose/src/lib.rs
index 81cdad56a..2942fb962 100644
--- a/crates/compose/src/lib.rs
+++ b/crates/compose/src/lib.rs
@@ -6159,21 +6159,72 @@ fn vertical_justify(
                 shift[k] <= 0.0 || ((k == n || l.baseline + l.descent + shift[k] <= limit + 1e-9) && in_outline(l, shift[k]))
             }) && clear(shift)
         };
+        // The room in 0..=`top` at which a moved line's band (from its top down to its baseline, or
+        // to its descent where `inside`), widened by the outline's inset, reaches one of the
+        // outline's corner heights: between two of these each line's fit changes only along the
+        // outline's straight edges. Empty when there are more than `MAX_BAND_BREAKS`.
+        const MAX_BAND_BREAKS: usize = 256;
+        let band_breaks = |o: &FrameOutline, top: f64| -> Vec<f64> {
+            let corners = o.corner_heights();
+            let d = o.inset();
+            // Each row's shift is linear in the room, apart from Justify's turn where the space
+            // between paragraphs reaches the Paragraph Spacing Limit.
+            let mut knots = vec![0.0, top];
+            let turn = gaps as f64 * para_limit;
+            if f.opts.vertical_justification == VerticalJustification::Justify && turn > 0.0 && turn < top {
+                knots.insert(1, turn);
+            }
+            let at: Vec<Vec<f64>> = knots.iter().map(|&c| shifts(c)).collect();
+            let mut out = Vec::new();
+            for (&i, &k) in idx.iter().zip(&rows) {
+                let l = &ft.lines[i];
+                let desc = if inside { l.descent.max(0.0) } else { 0.0 };
+                for &y in &corners {
+                    for v in [y + d - (l.baseline - l.ascent), y - d - (l.baseline + desc)] {
+                        for (c, s) in knots.windows(2).zip(at.windows(2)) {
+                            let (s0, s1) = (s[0][k], s[1][k]);
+                            if s1 > s0 && v > s0 && v < s1 {
+                                out.push(c[0] + (v - s0) * (c[1] - c[0]) / (s1 - s0));
+                            }
+                        }
+                    }
+                    if out.len() > MAX_BAND_BREAKS {
+                        return Vec::new();
+                    }
+                }
+            }
+            out
+        };
         // In a rectangular frame fit decreases monotonically as the shift grows. A shaped
         // frame can narrow and widen again, so scan from the largest shift before refining the
-        // first fitting interval. This also bounds the room used for baseline-grid quantization
-        // and preserves clearance from fixed and anchor-following wraps.
+        // first fitting interval. The scan takes even steps, the band breaks and a room on each
+        // side of every band break, so a band that fits over less room than one step is found
+        // too. This also bounds the room used for baseline-grid quantization and preserves
+        // clearance from fixed and anchor-following wraps.
         let most_room = |top: f64| -> f64 {
             if fits(&shifts(top)) {
                 return top;
             }
-            let (mut lo, mut hi) = if f.outline.is_some() {
+            let (mut lo, mut hi) = if let Some(o) = &f.outline {
                 let steps = top.ceil().clamp(64.0, 512.0) as usize;
+                // Each try is marked when it is a band break; only the gaps next to a break get a
+                // try in their middle.
+                let mut marked: Vec<(f64, bool)> = (0..steps).map(|j| (top * j as f64 / steps as f64, false)).collect();
+                marked.extend(band_breaks(o, top).into_iter().map(|c| (c, true)));
+                marked.push((top, false));
+                marked.sort_by(|a, b| a.0.total_cmp(&b.0));
+                marked.dedup_by(|a, b| {
+                    let same = (a.0 - b.0).abs() < 1e-9;
+                    b.1 |= same && a.1;
+                    same
+                });
+                let mut tries: Vec<f64> = marked.windows(2).filter(|w| w[0].1 || w[1].1).map(|w| (w[0].0 + w[1].0) / 2.0).collect();
+                tries.extend(marked.iter().map(|m| m.0));
+                tries.sort_by(f64::total_cmp);
                 let mut found = (0.0, top);
-                for j in 1..=steps {
-                    let candidate = top * (steps - j) as f64 / steps as f64;
-                    if fits(&shifts(candidate)) {
-                        found = (candidate, top * (steps - j + 1) as f64 / steps as f64);
+                for w in tries.windows(2).rev() {
+                    if fits(&shifts(w[0])) {
+                        found = (w[0], w[1]);
                         break;
                     }
                 }
diff --git a/crates/compose/src/outline.rs b/crates/compose/src/outline.rs
index dd1f59c0e..dc7d97ac3 100644
--- a/crates/compose/src/outline.rs
+++ b/crates/compose/src/outline.rs
@@ -71,6 +71,20 @@ impl FrameOutline {
         FrameOutline { edges: self.edges.iter().map(|&(a, b)| (xf * a, xf * b)).collect(), inset: self.inset }
     }
 
+    /// The distance kept between text and the outline.
+    pub fn inset(&self) -> f64 {
+        self.inset
+    }
+
+    /// The heights of the outline's corners, sorted and without repeats: the inside intervals of a
+    /// scanline change linearly between two of them.
+    pub fn corner_heights(&self) -> Vec<f64> {
+        let mut ys: Vec<f64> = self.edges.iter().map(|(a, _)| a.y).collect();
+        ys.sort_by(f64::total_cmp);
+        ys.dedup_by(|a, b| (*a - *b).abs() < 1e-9);
+        ys
+    }
+
     /// The parts of `[x0, x1]` inside the outline over the whole band `[y0, y1]`, at least the
     /// inset away from it: the inside intervals at every height of the band are intersected, and
     /// the inset is kept by testing the heights within the inset above and below the band, each
diff --git a/crates/compose/src/tests.rs b/crates/compose/src/tests.rs
index a0eac4061..e28b1265a 100644
--- a/crates/compose/src/tests.rs
+++ b/crates/compose/src/tests.rs
@@ -3206,6 +3206,39 @@ fn vertical_justification_lets_earlier_descenders_cross_a_shaped_frame() {
     }
 }
 
+/// In a tall shaped frame, Bottom finds a band that the line fits in over less room than one step
+/// of an even scan: in a frame that is half width from 40 pt down, apart from a full-width band
+/// only 0.25 pt taller than the line at 1,800 pt, the line moves into that band.
+#[test]
+fn vertical_justification_finds_a_narrow_band_in_a_tall_shaped_frame() {
+    use designcraft_doc::VerticalJustification::{self, Bottom, Top};
+    use designcraft_geom::{Anchor, PathData, Point, SubPath};
+    let compose_with = |pts: &[(f64, f64)], mode: VerticalJustification| -> Vec<Line> {
+        let (mut d, sid, fid) = doc_with("Typography", Rect::new(0.0, 0.0, 300.0, 2000.0), ParaAttrs::default());
+        let it = d.item_mut(fid).unwrap();
+        if !pts.is_empty() {
+            it.path = PathData::single(SubPath { anchors: pts.iter().map(|&(x, y)| Anchor::corner(Point::new(x, y))).collect(), closed: true });
+        }
+        let o = &mut it.text_frame_mut().unwrap().options;
+        o.vertical_justification = mode;
+        o.inset = [0.0; 4];
+        assert_eq!(frame_specs(&d, sid)[0].outline.is_some(), !pts.is_empty());
+        let cs = compose_story(&d, sid, &ComposeOptions::default());
+        assert!(!cs.is_overset(), "{mode:?}");
+        all_lines(&cs).into_iter().cloned().collect()
+    };
+    let ascent = compose_with(&[], Top)[0].ascent;
+    assert!(ascent > 1.0, "ascent {ascent}");
+    let (y0, y1) = (1800.0, 1800.0 + ascent + 0.25);
+    let pts =
+        [(0.0, 0.0), (300.0, 0.0), (300.0, 40.0), (150.0, 40.0), (150.0, y0), (300.0, y0), (300.0, y1), (150.0, y1), (150.0, 2000.0), (0.0, 2000.0)];
+    let lines = compose_with(&pts, Bottom);
+    assert_eq!(lines.len(), 1, "{lines:?}");
+    let l = &lines[0];
+    assert!((l.x1 - 300.0).abs() < 1e-6, "slot {l:?}");
+    assert!(l.baseline - l.ascent >= y0 - 1e-6 && l.baseline <= y1 + 1e-6, "baseline at {}, band {y0}..{y1}", l.baseline);
+}
+
 /// In a shaped frame with a text wrap under the text, Center, Bottom and Justify keep the lines
 /// inside the outline and out of the wrap together: in a triangle that widens downward, Bottom and
 /// Justify put the last baseline on the wrap's top and Center moves half as far; in one that