diff --git a/crates/fj-kernel/src/algorithms/approx/curve.rs b/crates/fj-kernel/src/algorithms/approx/curve.rs
index 708bec430..c0e7dafa2 100644
--- a/crates/fj-kernel/src/algorithms/approx/curve.rs
+++ b/crates/fj-kernel/src/algorithms/approx/curve.rs
@@ -102,7 +102,7 @@ fn number_of_vertices_for_circle(
 }
 
 /// The range on which a curve should be approximated
-#[derive(Clone, Copy)]
+#[derive(Clone, Copy, Debug)]
 pub struct RangeOnCurve {
     /// The boundary of the range
     ///
diff --git a/crates/fj-kernel/src/algorithms/reverse/cycle.rs b/crates/fj-kernel/src/algorithms/reverse/cycle.rs
index 7ec00c5bc..45e67bc30 100644
--- a/crates/fj-kernel/src/algorithms/reverse/cycle.rs
+++ b/crates/fj-kernel/src/algorithms/reverse/cycle.rs
@@ -8,7 +8,7 @@ impl Reverse for Cycle {
 
         let mut edges = self
             .into_edges()
-            .map(|edge| edge.reverse())
+            .map(|edge| edge.reverse_including_curve())
             .collect::<Vec<_>>();
 
         edges.reverse();
diff --git a/crates/fj-kernel/src/algorithms/reverse/edge.rs b/crates/fj-kernel/src/algorithms/reverse/edge.rs
index 623a67c12..b64d59753 100644
--- a/crates/fj-kernel/src/algorithms/reverse/edge.rs
+++ b/crates/fj-kernel/src/algorithms/reverse/edge.rs
@@ -4,9 +4,6 @@ use super::Reverse;
 
 impl Reverse for Edge {
     fn reverse(self) -> Self {
-        Edge::from_curve_and_vertices(
-            self.curve().reverse(),
-            self.vertices().reverse(),
-        )
+        Edge::from_curve_and_vertices(*self.curve(), self.vertices().reverse())
     }
 }
diff --git a/crates/fj-kernel/src/algorithms/sweep/edge.rs b/crates/fj-kernel/src/algorithms/sweep/edge.rs
index bb63a6064..46f6d6148 100644
--- a/crates/fj-kernel/src/algorithms/sweep/edge.rs
+++ b/crates/fj-kernel/src/algorithms/sweep/edge.rs
@@ -44,7 +44,7 @@ fn create_non_continuous_side_face(
     color: Color,
 ) -> Face {
     let edge = if path.is_negative_direction() {
-        edge.reverse()
+        edge.reverse_including_curve()
     } else {
         *edge
     };
diff --git a/crates/fj-kernel/src/objects/edge.rs b/crates/fj-kernel/src/objects/edge.rs
index 0e92e8f26..d1cb7bbf3 100644
--- a/crates/fj-kernel/src/objects/edge.rs
+++ b/crates/fj-kernel/src/objects/edge.rs
@@ -72,6 +72,34 @@ impl Edge {
         Self::new(curve, vertices, global)
     }
 
+    /// Reverse the edge, including the curve
+    ///
+    /// # Implementation Note
+    ///
+    /// It would be much nicer to just reverse the edge normally everywhere, but
+    /// we can't do that, until #695 is addressed:
+    /// <https://github.com/hannobraun/Fornjot/issues/695>
+    pub fn reverse_including_curve(self) -> Self {
+        let vertices = VerticesOfEdge(self.vertices.get().map(|[a, b]| {
+            [
+                Vertex::new(
+                    -b.position(),
+                    b.curve().reverse(),
+                    *b.surface_form(),
+                    *b.global_form(),
+                ),
+                Vertex::new(
+                    -a.position(),
+                    a.curve().reverse(),
+                    *a.surface_form(),
+                    *a.global_form(),
+                ),
+            ]
+        }));
+
+        Self::from_curve_and_vertices(self.curve().reverse(), vertices)
+    }
+
     /// Access the curve that defines the edge's geometry
     ///
     /// The edge can be a segment of the curve that is bounded by two vertices,
@@ -211,22 +239,7 @@ impl VerticesOfEdge<Vertex> {
     ///
     /// Makes sure that the local coordinates are still correct.
     pub fn reverse(self) -> Self {
-        Self(self.0.map(|[a, b]| {
-            [
-                Vertex::new(
-                    -b.position(),
-                    b.curve().reverse(),
-                    *b.surface_form(),
-                    *b.global_form(),
-                ),
-                Vertex::new(
-                    -a.position(),
-                    a.curve().reverse(),
-                    *a.surface_form(),
-                    *a.global_form(),
-                ),
-            ]
-        }))
+        Self(self.0.map(|[a, b]| [b, a]))
     }
 
     /// Convert this instance into its global variant