diff --git a/crates/geom/src/region.rs b/crates/geom/src/region.rs
index 085556525..cb5d57877 100644
--- a/crates/geom/src/region.rs
+++ b/crates/geom/src/region.rs
@@ -479,7 +479,9 @@ fn nearest_curve(polys: &[Vec<Vec2>], i: usize, e: Vec2, snap: f64, tol: f64, bu
             continue;
         }
         // A curve with no segment costs a visit too, so many of them can't multiply the searches.
-        *budget = budget.checked_sub(1).ok_or(())?;
+        if other.len() < 2 {
+            *budget = budget.checked_sub(1).ok_or(())?;
+        }
         for (k, w) in other.windows(2).enumerate() {
             if *budget == 0 {
                 return Err(());