diff --git a/crates/path/src/ops.rs b/crates/path/src/ops.rs
index 0e59046e6..ebc55505c 100644
--- a/crates/path/src/ops.rs
+++ b/crates/path/src/ops.rs
@@ -448,11 +448,16 @@ struct Sample {
 /// output keeps a short stack from multiplying a simple path into billions of points.
 pub const MAX_OPERATOR_SEGMENTS: usize = 1 << 20;
 
-/// `want` pieces (or copies) per input segment, reduced so the whole output stays within
-/// [`MAX_OPERATOR_SEGMENTS`] (never below 1, so the input itself always passes through).
+/// `want` pieces (or copies) per input segment, reduced so the whole output (segments times
+/// pieces, plus per-subpath overhead) stays within [`MAX_OPERATOR_SEGMENTS`] (never below 1, so the input itself always passes through).
 fn pieces_within_budget(paths: &[BezPath], want: usize) -> usize {
-    let segs: usize = paths.iter().map(|p| p.elements().len()).sum();
-    want.min(MAX_OPERATOR_SEGMENTS / segs.max(1)).max(1)
+    // Count what is subdivided (drawn segments) and keep room for each subpath's own MoveTo/Close.
+    let (mut segs, mut overhead) = (0usize, 0usize);
+    for sub in paths.iter().flat_map(subs) {
+        segs = segs.saturating_add(sub.segs.len());
+        overhead = overhead.saturating_add(2);
+    }
+    want.min(MAX_OPERATOR_SEGMENTS.saturating_sub(overhead) / segs.max(1)).max(1)
 }
 
 /// Split every segment into `m` pieces of equal arc length. Original vertices get the average of
diff --git a/crates/path/src/ops/tests.rs b/crates/path/src/ops/tests.rs
index de8321be6..5735d5724 100644
--- a/crates/path/src/ops/tests.rs
+++ b/crates/path/src/ops/tests.rs
@@ -438,3 +438,18 @@ fn stacked_expanding_operators_stay_within_the_segment_budget() {
     // Within the budget nothing changes: 4 segments × 11 pieces.
     assert_eq!(vertex_count(&zigzag(&[sq(0.0, 0.0, 100.0)], 1.0, 10.0, false)[0]), 44);
 }
+
+#[test]
+fn many_short_open_paths_keep_their_requested_detail_within_the_budget() {
+    // 1000 open lines at 1000 ridges: 1,001,000 segments fit the budget, so nothing is reduced.
+    let lines: Vec<BezPath> = (0..1000)
+        .map(|i| {
+            let mut p = BezPath::new();
+            p.move_to((0.0, i as f64));
+            p.line_to((100.0, i as f64));
+            p
+        })
+        .collect();
+    let z = zigzag(&lines, 1.0, 1000.0, false);
+    assert!(z.iter().all(|q| q.elements().len() == 1 + 1001));
+}