diff --git a/crates/fj-core/src/algorithms/approx/curve/segment.rs b/crates/fj-core/src/algorithms/approx/curve/segment.rs
index d3735ce36..631a8923d 100644
--- a/crates/fj-core/src/algorithms/approx/curve/segment.rs
+++ b/crates/fj-core/src/algorithms/approx/curve/segment.rs
@@ -79,10 +79,8 @@ impl CurveApproxSegment {
         );
 
         self.boundary = self.boundary.subset(boundary);
-
-        let [min, max] = self.boundary.inner;
         self.points
-            .retain(|point| point.local_form > min && point.local_form < max);
+            .retain(|point| self.boundary.contains(point.local_form));
     }
 
     /// Merge the provided segment into this one
@@ -112,7 +110,7 @@ impl CurveApproxSegment {
         self.points.retain(|point| {
             // Only retain points that don't overlap with the other segment, or
             // we might end up with duplicates.
-            point.local_form < other_min || point.local_form > other_max
+            !other.boundary.contains(point.local_form)
         });
         self.points.extend(&other.points);
         self.points.sort();
diff --git a/crates/fj-core/src/geometry/boundary.rs b/crates/fj-core/src/geometry/boundary.rs
index a7d2dea5b..d86a4eb84 100644
--- a/crates/fj-core/src/geometry/boundary.rs
+++ b/crates/fj-core/src/geometry/boundary.rs
@@ -65,6 +65,12 @@ impl CurveBoundary<Point<1>> {
         min >= max
     }
 
+    /// Indicate whether the boundary contains the given element
+    pub fn contains(&self, point: Point<1>) -> bool {
+        let [min, max] = self.inner;
+        point > min && point < max
+    }
+
     /// Indicate whether the boundary overlaps another
     ///
     /// Boundaries that touch (i.e. their closest boundary elements are equal)