diff --git a/crates/fj-core/src/geometry/boundary.rs b/crates/fj-core/src/geometry/boundary.rs
index bb5ed9935..8a6eef11a 100644
--- a/crates/fj-core/src/geometry/boundary.rs
+++ b/crates/fj-core/src/geometry/boundary.rs
@@ -31,12 +31,18 @@ impl<T: CurveBoundaryElement> CurveBoundary<T> {
     /// Normalize the boundary
     ///
     /// Returns a new instance of this struct, which has the bounding elements
-    /// in a defined order. This can be used to compare a boundary while
-    /// disregarding its direction.
+    /// in a defined order, alongside a boolean that indicates whether the new
+    /// instance is different from the original one.
+    ///
+    /// This can be used to compare a boundary while disregarding its direction.
     #[must_use]
-    pub fn normalize(mut self) -> Self {
-        self.inner.sort();
-        self
+    pub fn normalize(self) -> (Self, bool) {
+        let [a, b] = &self.inner;
+        if a > b {
+            (self.reverse(), true)
+        } else {
+            (self, false)
+        }
     }
 }
 
diff --git a/crates/fj-core/src/validate/shell.rs b/crates/fj-core/src/validate/shell.rs
index eb1f1f328..c87b92542 100644
--- a/crates/fj-core/src/validate/shell.rs
+++ b/crates/fj-core/src/validate/shell.rs
@@ -235,6 +235,7 @@ impl ShellValidationError {
                                 .bounding_vertices_of_edge(edge)
                                 .expect("Expected edge to be part of shell")
                                 .normalize()
+                                .0
                         };
 
                         bounding_vertices_of(edge_a)
@@ -314,7 +315,8 @@ impl ShellValidationError {
                         .expect(
                             "Cycle should provide bounds of its own half-edge",
                         )
-                        .normalize();
+                        .normalize()
+                        .0;
 
                     let edge = (curve, bounding_vertices);
 
@@ -394,7 +396,8 @@ impl ShellValidationError {
                         .expect(
                             "Just got edge from this cycle; must be part of it",
                         )
-                        .normalize();
+                        .normalize()
+                        .0;
 
                     edges_by_coincidence
                         .entry((curve, boundary))