diff --git a/crates/compose/src/lib.rs b/crates/compose/src/lib.rs
index b83f479fe..9c423cec0 100644
--- a/crates/compose/src/lib.rs
+++ b/crates/compose/src/lib.rs
@@ -1858,8 +1858,14 @@ fn position_line(input: PositionLineInput<'_, '_>) -> LinePosition {
         if cur.last_baseline.is_some() {
             baseline += cur.last_reference - reference;
         }
-        let grid = f.grid.filter(|&(_, inc)| {
-            inc > 0.0 && inc.is_finite() && (pp.grid_align == GridAlign::AllLines || (pp.grid_align == GridAlign::FirstLineOnly && line_no == 0))
+        // A step so small that the column holds more steps than an f64 can count is no grid: the
+        // line is placed as it is without one.
+        let countable = |g_start: f64, inc: f64| [baseline, col.y0, col.y1].iter().all(|y| ((y - g_start) / inc).is_finite());
+        let grid = f.grid.filter(|&(g_start, inc)| {
+            inc > 0.0
+                && inc.is_finite()
+                && countable(g_start, inc)
+                && (pp.grid_align == GridAlign::AllLines || (pp.grid_align == GridAlign::FirstLineOnly && line_no == 0))
         });
         if let Some((g_start, inc)) = grid {
             let n = pp.grid_gyoudori.min(grid::MAX_GYOUDORI);
@@ -6151,9 +6157,26 @@ fn vertical_justify(
                 // The last baseline stays above the bottom of the text, and the rows above it fit.
                 let most = (space / inc + 1e-9).floor().min((room / unit + 1e-9).floor()).max(0.0);
                 // Bottom and Justify take the lowest grid line, Center the one nearest the middle.
-                let mut steps = if center { (space / 2.0 / inc).round().min(most) } else { most };
-                if steps > 0.0 && !fits(&shifts(steps * unit)) {
-                    steps -= 1.0;
+                let target = if center { (space / 2.0 / inc).round().min(most) } else { most };
+                // A shaped frame can narrow and widen again, so the target step may not fit: take
+                // the fitting step nearest it, up to `most` (the lower one on a tie, and no step
+                // when that is as near), and leave the lines in place when none within
+                // `MAX_GRID_TRIES` steps of it fits.
+                const MAX_GRID_TRIES: usize = 512;
+                let mut steps = 0.0;
+                for d in 0..MAX_GRID_TRIES {
+                    let (below, above) = (target - d as f64, target + d as f64);
+                    if below <= 0.0 {
+                        break;
+                    }
+                    if fits(&shifts(below * unit)) {
+                        steps = below;
+                        break;
+                    }
+                    if d > 0 && above <= most && fits(&shifts(above * unit)) {
+                        steps = above;
+                        break;
+                    }
                 }
                 // With no step taken the lines stay put, even when Center's doubled step overflows.
                 shifts(if steps > 0.0 { steps * unit } else { 0.0 })
diff --git a/crates/compose/src/tests.rs b/crates/compose/src/tests.rs
index 41a734f4c..59777d657 100644
--- a/crates/compose/src/tests.rs
+++ b/crates/compose/src/tests.rs
@@ -2799,6 +2799,25 @@ fn vertical_justification_keeps_grid_aligned_lines_on_the_grid() {
     let (_, first_only, _) = compose_with(Bottom, GridAlign::FirstLineOnly);
     assert!(first_only.iter().all(|&b| on_grid(b, grid)), "Bottom, first lines only: {first_only:?}");
 
+    // Justify with a paragraph that wraps: with all lines aligned the last line lands on the grid;
+    // with first lines only it is not a first line, so it goes down to the bottom inset.
+    let wrapped = "The first line of this paragraph sits on the baseline grid, and the lines after it keep the leading they have.";
+    let justify_wrapped = |align: GridAlign| {
+        let (lines, _) = grid_doc(wrapped, ParaAttrs { grid_align: Some(align), ..Default::default() }, |d, sid| {
+            let spec = frame_specs(d, sid).remove(0);
+            d.item_mut(spec.id).unwrap().text_frame_mut().unwrap().options.vertical_justification = Justify;
+        });
+        lines.iter().map(|l| l.baseline).collect::<Vec<_>>()
+    };
+    let all = justify_wrapped(GridAlign::AllLines);
+    assert!(all.len() >= 2, "the paragraph wraps: {all:?}");
+    let last = all[all.len() - 1];
+    assert!(on_grid(last, grid) && last <= area.y1 + 1e-6 && last > area.y1 - inc, "Justify, all lines: last baseline {last}");
+    let first_lines = justify_wrapped(GridAlign::FirstLineOnly);
+    assert!(first_lines.len() >= 2, "the paragraph wraps: {first_lines:?}");
+    let last = first_lines[first_lines.len() - 1];
+    assert!((last - area.y1).abs() < 1e-6 && !on_grid(last, grid), "Justify, first lines only: last baseline {last}, inset at {}", area.y1);
+
     // Without grid alignment the last baseline goes down to the bottom inset.
     let (_, free, _) = compose_with(Bottom, GridAlign::None);
     assert!((free[2] - area.y1).abs() < 1e-6, "Bottom without the grid: {free:?}");
@@ -2839,6 +2858,69 @@ fn vertical_justification_with_an_extreme_grid_increment_stays_finite() {
     // A step far larger than the room: the line does not move.
     let (_, b) = compose_with(Center, 1e308);
     assert!((b - natural).abs() < 1e-6, "Center with a huge increment: baseline {b}, natural {natural}");
+
+    // A grid that starts away from the line, with a step too small to count the distance: the line
+    // is placed as it is without a grid.
+    for mode in [Top, Bottom, Center, Justify] {
+        let mut area = Rect::ZERO;
+        let (lines, _) = grid_doc("One", ParaAttrs { grid_align: Some(GridAlign::AllLines), ..Default::default() }, |d, sid| {
+            let spec = frame_specs(d, sid).remove(0);
+            area = spec.area;
+            let opts = &mut d.item_mut(spec.id).unwrap().text_frame_mut().unwrap().options;
+            opts.baseline_grid = Some(designcraft_doc::FrameBaselineGrid::new(start - 5.0, 1e-310));
+            opts.vertical_justification = mode;
+        });
+        let b = lines[0].baseline;
+        assert!(b.is_finite() && b >= natural - 1e-6 && b <= area.y1 + 1e-6, "{mode:?}, grid away from the line: baseline {b}, text area {area:?}");
+        if mode == Top {
+            assert!((b - natural).abs() < 1e-6, "Top, grid away from the line: baseline {b}, natural {natural}");
+        }
+    }
+}
+
+/// In a shaped frame that narrows and widens again, Align to Baseline Grid takes the grid step
+/// nearest the place Bottom or Center would choose at which the line's slot fits the outline:
+/// Bottom goes up past steps in the narrow part, and Center goes down a step when the step nearest
+/// the middle is in the narrow part and the next one fits.
+#[test]
+fn vertical_justification_on_the_grid_skips_steps_that_leave_a_shaped_frame() {
+    use designcraft_doc::GridAlign;
+    use designcraft_doc::VerticalJustification::{self, Bottom, Center, Top};
+    use designcraft_geom::{Anchor, PathData, Point, SubPath};
+    // Full width down to 100 pt, a waist at 150 pt, full width again from 200 to 230 pt, then a
+    // point at 300 pt.
+    let pts = [(0.0, 0.0), (300.0, 0.0), (300.0, 100.0), (200.0, 150.0), (300.0, 200.0), (300.0, 230.0), (150.0, 300.0)];
+    let pts: Vec<(f64, f64)> = pts.iter().copied().chain([(0.0, 230.0), (0.0, 200.0), (100.0, 150.0), (0.0, 100.0)]).collect();
+    let compose_with = |mode: VerticalJustification, inc: f64| {
+        let para = ParaAttrs { grid_align: Some(GridAlign::AllLines), ..Default::default() };
+        let (mut d, sid, fid) = doc_with("Typography", Rect::new(0.0, 0.0, 300.0, 300.0), para);
+        let it = d.item_mut(fid).unwrap();
+        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.inset = [0.0; 4];
+        o.baseline_grid = Some(designcraft_doc::FrameBaselineGrid::new(0.0, inc));
+        o.vertical_justification = mode;
+        let grid = frame_specs(&d, sid)[0].grid.unwrap();
+        let cs = compose_story(&d, sid, &ComposeOptions::default());
+        let l = all_lines(&cs)[0];
+        (grid, l.baseline, l.baseline - l.ascent)
+    };
+    let lower = |b: f64, band_top: f64| band_top >= 200.0 - 1e-6 && b <= 230.0 + 1e-6;
+
+    // A 40 pt grid: the lowest room ends between 160 and 200 pt, and the steps above it down to
+    // 120 pt put the line in the waist.
+    let (grid, top, _) = compose_with(Top, 40.0);
+    assert!(on_grid(top, grid), "Top: baseline {top} on the grid {grid:?}");
+    let (_, b, band_top) = compose_with(Bottom, 40.0);
+    assert!(on_grid(b, grid), "Bottom: baseline {b} on the grid {grid:?}");
+    assert!(b <= 100.0 + 1e-6 || lower(b, band_top), "Bottom: the line's band {band_top}..{b} reaches into the narrow part");
+    assert!(b > top, "Bottom moves the line down a grid step that fits: {b}, Top at {top}");
+
+    // A 45 pt grid: the step nearest the middle puts the baseline at 180 pt, in the waist; the
+    // step below it fits in the lower full-width part.
+    let (grid, b, band_top) = compose_with(Center, 45.0);
+    assert!(on_grid(b, grid), "Center: baseline {b} on the grid {grid:?}");
+    assert!(lower(b, band_top), "Center: the line's band {band_top}..{b} is not in the lower full-width part");
 }
 
 /// A corner radius leaves a Cap Height first line where it sits in a rectangular frame, with Top