diff --git a/crates/geom/src/hit.rs b/crates/geom/src/hit.rs
index 944ded3e..6115a96c 100644
--- a/crates/geom/src/hit.rs
+++ b/crates/geom/src/hit.rs
@@ -15,7 +15,7 @@ pub fn fill_contains(path: &BezPath, rule: FillRule, p: Point) -> bool {
 
 /// Distance from `p` to the nearest point on the path outline.
 pub fn distance_to_outline(path: &BezPath, p: Point) -> f64 {
-    path.segments().map(|s| s.nearest(p, 1e-6).distance_sq).fold(f64::INFINITY, f64::min).sqrt()
+    path.segments().map(|s| s.nearest(p, 1e-9).distance_sq).fold(f64::INFINITY, f64::min).sqrt()
 }
 
 /// Is `p` within `tol` of the path's stroke of width `width`?
@@ -91,3 +91,26 @@ mod tests {
         assert!(intersects_rect(&l, Rect::new(4.0, 0.0, 6.0, 10.0)));
     }
 }
+
+#[cfg(test)]
+mod regress_tests {
+    use super::*;
+    use kurbo::{CubicBez, ParamCurve};
+
+    /// A cubic whose handles sit on its anchors on one side (cusp-like): points on the curve are
+    /// at distance ~0 (proptest regression).
+    #[test]
+    fn nearest_on_degenerate_cubic() {
+        let c = CubicBez::new(
+            (131.69052599341336, 172.64518298885875),
+            (104.00879084385166, 172.64518298885875),
+            (145.71215277397286, 141.82358989609716),
+            (131.4188160942415, 162.38678549385997),
+        );
+        let mut bp = BezPath::new();
+        bp.move_to(c.p0);
+        bp.curve_to(c.p1, c.p2, c.p3);
+        let worst = (0..=200).map(|i| distance_to_outline(&bp, c.eval(i as f64 / 200.0))).fold(0.0, f64::max);
+        assert!(worst < 1e-6, "{worst}");
+    }
+}