diff --git a/crates/pathops/src/edit.rs b/crates/pathops/src/edit.rs
index da8e5e4d8..17b231a5d 100644
--- a/crates/pathops/src/edit.rs
+++ b/crates/pathops/src/edit.rs
@@ -146,8 +146,9 @@ fn simplify_subpath(sp: &SubPath, opts: &SimplifyOptions) -> Option<SubPath> {
             // ends and those lines enclose an area: with straight lines they are the result, and without
             // them the loop stays as it is. When no split within those limits encloses an area, the loop
             // stays as it is, or with straight lines each curved segment becomes the lines between its
-            // samples, up to `MAX_RUN_RESULT` lines in all. A loop whose points are all in line keeps the
-            // lines of the refit.
+            // samples, up to `MAX_RUN_RESULT` lines in all with the line segments; when that leaves no
+            // line for some curved segment, the loop stays as it is. A loop whose points are all in line
+            // keeps the lines of the refit.
             let near = |c: &CubicBez| [c.p1, c.p2].iter().all(|&p| Line::new(c.p0, c.p3).nearest(p, 1e-9).distance_sq.sqrt() <= opts.tolerance);
             let curved = segs.iter().filter(|s| !s.line).count();
             for k in 1..=10u32 {
@@ -174,7 +175,9 @@ fn simplify_subpath(sp: &SubPath, opts: &SimplifyOptions) -> Option<SubPath> {
             if !opts.straight_lines {
                 return Some(sp.clone());
             }
-            let room = (MAX_RUN_RESULT / curved.max(1)).min(MAX_SEGMENT_SAMPLES);
+            let Some(room) = sample_room(curved, n - curved) else {
+                return Some(sp.clone());
+            };
             let mut lines: Vec<Seg> = Vec::new();
             for s in &segs {
                 if s.line {
@@ -192,6 +195,17 @@ fn simplify_subpath(sp: &SubPath, opts: &SimplifyOptions) -> Option<SubPath> {
     Some(if opts.straight_lines { s } else { no_worse(sp, s) })
 }
 
+/// Most lines between samples of each of `curved` segments, so that they and the `kept` line segments
+/// make at most [`MAX_RUN_RESULT`] lines, and each has at most [`MAX_SEGMENT_SAMPLES`]. `None` when
+/// that leaves no line for some curved segment.
+fn sample_room(curved: usize, kept: usize) -> Option<usize> {
+    let left = MAX_RUN_RESULT.checked_sub(kept)?;
+    if curved > left {
+        return None;
+    }
+    Some((left / curved.max(1)).min(MAX_SEGMENT_SAMPLES))
+}
+
 /// How far a segment may be from the lines between its samples, as a share of the tolerance.
 const SAMPLE_GAP: f64 = 0.005;
 
@@ -1156,6 +1170,18 @@ mod tests {
         assert!(work <= 400 * pts.len(), "{work} steps for {} samples", pts.len());
     }
 
+    #[test]
+    fn the_samples_of_a_flat_loop_and_its_line_segments_stay_within_the_result_limit() {
+        for (curved, kept) in [(1, 0), (32, 1), (40, 1_000_000), (1_000, MAX_RUN_RESULT - 1_000), (3, MAX_RUN_RESULT - 7)] {
+            let room = sample_room(curved, kept).unwrap_or_else(|| panic!("{curved} curved, {kept} kept: no room"));
+            assert!((1..=MAX_SEGMENT_SAMPLES).contains(&room), "{curved} curved, {kept} kept: room {room}");
+            assert!(curved * room + kept <= MAX_RUN_RESULT, "{curved} curved, {kept} kept: room {room}");
+        }
+        assert_eq!(sample_room(32, 0), Some(MAX_SEGMENT_SAMPLES));
+        assert_eq!(sample_room(2, MAX_RUN_RESULT - 1), None);
+        assert_eq!(sample_room(1, MAX_RUN_RESULT + 5), None);
+    }
+
     #[test]
     fn smoothing_points_whose_arc_length_overflows_returns_every_point() {
         let pts: Vec<Point> = (0..40).map(|i| Point::new(if i % 2 == 0 { -1e308 } else { 1e308 }, f64::from(i))).collect();