diff --git a/crates/compose/src/breaker.rs b/crates/compose/src/breaker.rs
index 3b08e1050..16abde9cf 100644
--- a/crates/compose/src/breaker.rs
+++ b/crates/compose/src/breaker.rs
@@ -166,6 +166,11 @@ impl Item {
 
 const INF: f64 = 10000.0;
 
+/// A line whose natural width exceeds its measure by no more than this (points) still fits: frame
+/// widths and glyph advances are rounded, so a line that exactly fills the measure can come out a
+/// hair too wide.
+const FIT_EPS: f64 = 0.01;
+
 /// Does the glyph force a line end after it?
 /// A line may break between `a` and `b` in CJK text (any break next to an ideograph, kana or
 /// hangul), except where kinsoku forbids it: no line starts with closing punctuation, small
@@ -454,7 +459,10 @@ fn kp_pass(
                 y[t] = sy[b][t] - n.ty[t];
                 z[t] = sz[b][t] - n.tz[t];
             }
-            let (r, feasible) = tiered_ratio(target - l, y, z);
+            // A line that overruns its measure by a rounding error fits exactly.
+            let d = target - l;
+            let d = if d < 0.0 && d > -FIT_EPS { 0.0 } else { d };
+            let (r, feasible) = tiered_ratio(d, y, z);
             if feasible && !forced {
                 keep.push(a);
             } else {
@@ -664,7 +672,7 @@ pub fn greedy(glyphs: &[Glyph], hyph_after: &[bool], sp: &Spacing, width: &dyn F
                 continue;
             }
             let hang_r = right_hang(g, sp);
-            if x + g.adv - hang_r > w + shrink
+            if x + g.adv - hang_r > w + shrink + FIT_EPS
                 && i > start
                 && (last_ok.is_some() || glyphs.get(i - 1).is_none_or(|p| p.break_after != Some(false) && !p.no_break))
             {
@@ -690,7 +698,7 @@ pub fn greedy(glyphs: &[Glyph], hyph_after: &[bool], sp: &Spacing, width: &dyn F
                     last_ok = Some((i + 1, false));
                 } else if hyph_after[i] && may_hyphenate(hyphens) {
                     let hy = hyphen_width(g, &mut hy_cache) * if sp.optical { 1.0 - hang('-').1 } else { 1.0 };
-                    if x + hy <= w + shrink {
+                    if x + hy <= w + shrink + FIT_EPS {
                         last_ok = Some((i + 1, true));
                     }
                 }
diff --git a/crates/compose/src/tests.rs b/crates/compose/src/tests.rs
index 256d9a13c..4a500a344 100644
--- a/crates/compose/src/tests.rs
+++ b/crates/compose/src/tests.rs
@@ -1889,3 +1889,28 @@ fn vertical_lines_fit_the_em_box() {
         assert!((l.baseline - col.y0 - ascent).abs() < 1e-9, "{family}: {} {}", l.baseline, col.y0);
     }
 }
+
+/// Lines of `text` set in a frame `width` wide, with `tracking` on every character.
+fn tracked_lines(text: &str, width: f64, para: ParaAttrs, tracking: f64) -> Vec<Line> {
+    let (mut d, sid, _) = doc_with(text, Rect::new(0.0, 0.0, width, 4000.0), para);
+    d.story_mut(sid).unwrap().format_chars(0..text.len(), |f| f.over.tracking = Some(tracking));
+    let cs = compose_story(&d, sid, &ComposeOptions::default());
+    assert!(!cs.is_overset(), "overset at width {width}");
+    all_lines(&cs).into_iter().cloned().collect()
+}
+
+#[test]
+fn a_line_that_exactly_fills_the_measure_fits() {
+    use designcraft_doc::Composer;
+    let text = "#knowyourplastic";
+    let one = &tracked_lines(text, 1e5, ParaAttrs::default(), 0.0)[0];
+    // The measure a rounding error short of the natural width.
+    let width = one.end_x - one.x0 - 0.005;
+    for composer in [Composer::Paragraph, Composer::SingleLine] {
+        for align in [Align::Left, Align::LeftJustified] {
+            let para = ParaAttrs { composer: Some(composer), align: Some(align), ..Default::default() };
+            let lines = tracked_lines(text, width, para, 0.0);
+            assert_eq!(lines.len(), 1, "{composer:?} {align:?}: {:?}", lines.iter().map(|l| l.range.clone()).collect::<Vec<_>>());
+        }
+    }
+}