diff --git a/crates/fj-core/src/algorithms/mod.rs b/crates/fj-core/src/algorithms/mod.rs
index 2786c3f95..c7fa369d4 100644
--- a/crates/fj-core/src/algorithms/mod.rs
+++ b/crates/fj-core/src/algorithms/mod.rs
@@ -6,7 +6,6 @@
 pub mod approx;
 pub mod bounding_volume;
 pub mod intersect;
-pub mod reverse;
 pub mod sweep;
 pub mod transform;
 pub mod triangulate;
diff --git a/crates/fj-core/src/algorithms/reverse/face.rs b/crates/fj-core/src/algorithms/reverse/face.rs
deleted file mode 100644
index 089964680..000000000
--- a/crates/fj-core/src/algorithms/reverse/face.rs
+++ /dev/null
@@ -1,24 +0,0 @@
-use crate::{
-    objects::{Face, Region},
-    operations::Insert,
-    services::Services,
-    storage::Handle,
-};
-
-use super::Reverse;
-
-impl Reverse for Handle<Face> {
-    fn reverse(self, services: &mut Services) -> Self {
-        let exterior = self.region().exterior().clone().reverse(services);
-        let interiors = self
-            .region()
-            .interiors()
-            .map(|cycle| cycle.clone().reverse(services))
-            .collect::<Vec<_>>();
-
-        let region = Region::new(exterior, interiors, self.region().color())
-            .insert(services);
-
-        Face::new(self.surface().clone(), region).insert(services)
-    }
-}
diff --git a/crates/fj-core/src/algorithms/sweep/face.rs b/crates/fj-core/src/algorithms/sweep/face.rs
index 627dfc98e..4e1f5981a 100644
--- a/crates/fj-core/src/algorithms/sweep/face.rs
+++ b/crates/fj-core/src/algorithms/sweep/face.rs
@@ -4,10 +4,10 @@ use fj_math::{Scalar, Vector};
 use itertools::Itertools;
 
 use crate::{
-    algorithms::{reverse::Reverse, transform::TransformObject},
+    algorithms::transform::TransformObject,
     geometry::curve::GlobalPath,
     objects::{Cycle, Face, Region, Shell},
-    operations::{BuildCycle, Insert, JoinCycle},
+    operations::{BuildCycle, Insert, JoinCycle, Reverse},
     services::Services,
     storage::Handle,
 };
@@ -46,7 +46,7 @@ impl Sweep for Handle<Face> {
             if is_negative_sweep {
                 self.clone()
             } else {
-                self.clone().reverse(services)
+                self.clone().reverse(services).insert(services)
             }
         };
         faces.push(bottom_face.clone());
diff --git a/crates/fj-core/src/operations/mod.rs b/crates/fj-core/src/operations/mod.rs
index 4bd694904..5d43064e4 100644
--- a/crates/fj-core/src/operations/mod.rs
+++ b/crates/fj-core/src/operations/mod.rs
@@ -3,6 +3,7 @@
 mod build;
 mod insert;
 mod join;
+mod reverse;
 mod update;
 
 pub use self::{
@@ -18,6 +19,7 @@ pub use self::{
     },
     insert::{Insert, IsInserted, IsInsertedNo, IsInsertedYes},
     join::cycle::JoinCycle,
+    reverse::Reverse,
     update::{
         cycle::UpdateCycle, edge::UpdateHalfEdge, face::UpdateFace,
         region::UpdateRegion, shell::UpdateShell, sketch::UpdateSketch,
diff --git a/crates/fj-core/src/algorithms/reverse/cycle.rs b/crates/fj-core/src/operations/reverse/cycle.rs
similarity index 83%
rename from crates/fj-core/src/algorithms/reverse/cycle.rs
rename to crates/fj-core/src/operations/reverse/cycle.rs
index 5bef5fa7f..0db018408 100644
--- a/crates/fj-core/src/algorithms/reverse/cycle.rs
+++ b/crates/fj-core/src/operations/reverse/cycle.rs
@@ -4,13 +4,12 @@ use crate::{
     objects::{Cycle, HalfEdge},
     operations::Insert,
     services::Services,
-    storage::Handle,
 };
 
 use super::Reverse;
 
-impl Reverse for Handle<Cycle> {
-    fn reverse(self, services: &mut Services) -> Self {
+impl Reverse for Cycle {
+    fn reverse(&self, services: &mut Services) -> Self {
         let mut edges = self
             .half_edges()
             .cloned()
@@ -33,6 +32,6 @@ impl Reverse for Handle<Cycle> {
 
         edges.reverse();
 
-        Cycle::new(edges).insert(services)
+        Cycle::new(edges)
     }
 }
diff --git a/crates/fj-core/src/operations/reverse/face.rs b/crates/fj-core/src/operations/reverse/face.rs
new file mode 100644
index 000000000..deee5c378
--- /dev/null
+++ b/crates/fj-core/src/operations/reverse/face.rs
@@ -0,0 +1,28 @@
+use crate::{
+    objects::{Face, Region},
+    operations::Insert,
+    services::Services,
+};
+
+use super::Reverse;
+
+impl Reverse for Face {
+    fn reverse(&self, services: &mut Services) -> Self {
+        let exterior = self
+            .region()
+            .exterior()
+            .clone()
+            .reverse(services)
+            .insert(services);
+        let interiors = self
+            .region()
+            .interiors()
+            .map(|cycle| cycle.clone().reverse(services).insert(services))
+            .collect::<Vec<_>>();
+
+        let region = Region::new(exterior, interiors, self.region().color())
+            .insert(services);
+
+        Face::new(self.surface().clone(), region)
+    }
+}
diff --git a/crates/fj-core/src/algorithms/reverse/mod.rs b/crates/fj-core/src/operations/reverse/mod.rs
similarity index 72%
rename from crates/fj-core/src/algorithms/reverse/mod.rs
rename to crates/fj-core/src/operations/reverse/mod.rs
index 76a1f74d9..bb99a3bd7 100644
--- a/crates/fj-core/src/algorithms/reverse/mod.rs
+++ b/crates/fj-core/src/operations/reverse/mod.rs
@@ -6,7 +6,7 @@ mod cycle;
 mod face;
 
 /// Reverse the direction/orientation of an object
-pub trait Reverse: Sized {
+pub trait Reverse {
     /// Reverse the direction/orientation of the object
-    fn reverse(self, services: &mut Services) -> Self;
+    fn reverse(&self, services: &mut Services) -> Self;
 }
diff --git a/crates/fj-core/src/validate/face.rs b/crates/fj-core/src/validate/face.rs
index cf4f57303..ba059e9c9 100644
--- a/crates/fj-core/src/validate/face.rs
+++ b/crates/fj-core/src/validate/face.rs
@@ -71,10 +71,11 @@ impl FaceValidationError {
 #[cfg(test)]
 mod tests {
     use crate::{
-        algorithms::reverse::Reverse,
         assert_contains_err,
         objects::{Cycle, Face, Region},
-        operations::{BuildCycle, BuildFace, Insert, UpdateFace, UpdateRegion},
+        operations::{
+            BuildCycle, BuildFace, Insert, Reverse, UpdateFace, UpdateRegion,
+        },
         services::Services,
         validate::{FaceValidationError, Validate, ValidationError},
     };
@@ -106,7 +107,7 @@ mod tests {
                 .region()
                 .interiors()
                 .cloned()
-                .map(|cycle| cycle.reverse(&mut services))
+                .map(|cycle| cycle.reverse(&mut services).insert(&mut services))
                 .collect::<Vec<_>>();
 
             let region = Region::new(