diff --git a/crates/fj-core/src/geometry/geometry.rs b/crates/fj-core/src/geometry/geometry.rs
index 3b8f4ee00..00cd56e77 100644
--- a/crates/fj-core/src/geometry/geometry.rs
+++ b/crates/fj-core/src/geometry/geometry.rs
@@ -59,7 +59,7 @@ impl Geometry {
         surface: Handle<Surface>,
         geometry: SurfaceGeometry,
     ) {
-        self.surface.insert(surface.clone().into(), geometry);
+        self.surface.insert(surface.into(), geometry);
     }
 
     /// # Access the geometry of the provided surface
diff --git a/crates/fj-core/src/operations/build/cycle.rs b/crates/fj-core/src/operations/build/cycle.rs
index 118c09102..e0500a8d9 100644
--- a/crates/fj-core/src/operations/build/cycle.rs
+++ b/crates/fj-core/src/operations/build/cycle.rs
@@ -3,7 +3,7 @@ use itertools::Itertools;
 
 use crate::{
     objects::{Cycle, HalfEdge},
-    operations::{build::BuildHalfEdge, insert::Insert, update::UpdateCycle},
+    operations::{build::BuildHalfEdge, update::UpdateCycle},
     Core,
 };
 
@@ -40,7 +40,7 @@ pub trait BuildCycle {
             .map(Into::into)
             .circular_tuple_windows()
             .map(|(start, end)| {
-                HalfEdge::line_segment([start, end], None, core).insert(core)
+                HalfEdge::line_segment([start, end], None, core)
             });
 
         Cycle::new(edges)
diff --git a/crates/fj-core/src/operations/build/half_edge.rs b/crates/fj-core/src/operations/build/half_edge.rs
index b786e7a8e..0835c9d5d 100644
--- a/crates/fj-core/src/operations/build/half_edge.rs
+++ b/crates/fj-core/src/operations/build/half_edge.rs
@@ -29,15 +29,17 @@ pub trait BuildHalfEdge {
 
     /// Create a half-edge from its sibling
     fn from_sibling(
-        sibling: &HalfEdge,
+        sibling: &Handle<HalfEdge>,
         start_vertex: Handle<Vertex>,
-    ) -> HalfEdge {
+        core: &mut Core,
+    ) -> Handle<HalfEdge> {
         HalfEdge::new(
             sibling.path(),
             sibling.boundary().reverse(),
             sibling.curve().clone(),
             start_vertex,
         )
+        .insert(core)
     }
 
     /// Create an arc
@@ -50,7 +52,7 @@ pub trait BuildHalfEdge {
         end: impl Into<Point<2>>,
         angle_rad: impl Into<Scalar>,
         core: &mut Core,
-    ) -> HalfEdge {
+    ) -> Handle<HalfEdge> {
         let angle_rad = angle_rad.into();
         if angle_rad <= -Scalar::TAU || angle_rad >= Scalar::TAU {
             panic!("arc angle must be in the range (-2pi, 2pi) radians");
@@ -63,7 +65,7 @@ pub trait BuildHalfEdge {
         let boundary =
             [arc.start_angle, arc.end_angle].map(|coord| Point::from([coord]));
 
-        HalfEdge::unjoined(path, boundary, core)
+        HalfEdge::unjoined(path, boundary, core).insert(core)
     }
 
     /// Create a circle
@@ -71,12 +73,12 @@ pub trait BuildHalfEdge {
         center: impl Into<Point<2>>,
         radius: impl Into<Scalar>,
         core: &mut Core,
-    ) -> HalfEdge {
+    ) -> Handle<HalfEdge> {
         let path = SurfacePath::circle_from_center_and_radius(center, radius);
         let boundary =
             [Scalar::ZERO, Scalar::TAU].map(|coord| Point::from([coord]));
 
-        HalfEdge::unjoined(path, boundary, core)
+        HalfEdge::unjoined(path, boundary, core).insert(core)
     }
 
     /// Create a line segment
@@ -84,14 +86,14 @@ pub trait BuildHalfEdge {
         points_surface: [impl Into<Point<2>>; 2],
         boundary: Option<[Point<1>; 2]>,
         core: &mut Core,
-    ) -> HalfEdge {
+    ) -> Handle<HalfEdge> {
         let boundary =
             boundary.unwrap_or_else(|| [[0.], [1.]].map(Point::from));
         let path = SurfacePath::line_from_points_with_coords(
             boundary.zip_ext(points_surface),
         );
 
-        HalfEdge::unjoined(path, boundary, core)
+        HalfEdge::unjoined(path, boundary, core).insert(core)
     }
 }
 
diff --git a/crates/fj-core/src/operations/holes.rs b/crates/fj-core/src/operations/holes.rs
index d8d296cf8..6d878f2c7 100644
--- a/crates/fj-core/src/operations/holes.rs
+++ b/crates/fj-core/src/operations/holes.rs
@@ -10,7 +10,6 @@ use crate::{
 
 use super::{
     build::{BuildCycle, BuildHalfEdge, BuildRegion},
-    insert::Insert,
     join::JoinCycle,
     sweep::{SweepCache, SweepRegion},
     update::{UpdateCycle, UpdateFace, UpdateRegion, UpdateShell},
@@ -44,8 +43,7 @@ impl AddHole for Shell {
         path: impl Into<Vector<3>>,
         core: &mut Core,
     ) -> Self {
-        let entry =
-            HalfEdge::circle(location.position, radius, core).insert(core);
+        let entry = HalfEdge::circle(location.position, radius, core);
         let hole = Region::empty(core)
             .update_exterior(
                 |_, core| Cycle::empty().add_half_edges([entry.clone()], core),
@@ -94,8 +92,7 @@ impl AddHole for Shell {
     ) -> Self {
         let radius = radius.into();
 
-        let entry = HalfEdge::circle(entry_location.position, radius, core)
-            .insert(core);
+        let entry = HalfEdge::circle(entry_location.position, radius, core);
 
         let path = {
             let point = |location: &HoleLocation| {
diff --git a/crates/fj-core/src/operations/join/cycle.rs b/crates/fj-core/src/operations/join/cycle.rs
index e05a8effa..b90fcdb92 100644
--- a/crates/fj-core/src/operations/join/cycle.rs
+++ b/crates/fj-core/src/operations/join/cycle.rs
@@ -87,8 +87,8 @@ impl JoinCycle for Cycle {
         let half_edges = edges
             .into_iter()
             .circular_tuple_windows()
-            .map(|((prev_half_edge, _, _), (half_edge, curve, boundary))| {
-                HalfEdge::unjoined(curve, boundary, core)
+            .map(|((prev_half_edge, _, _), (half_edge, path, boundary))| {
+                HalfEdge::unjoined(path, boundary, core)
                     .update_curve(|_, _| half_edge.curve().clone(), core)
                     .update_start_vertex(
                         |_, _| prev_half_edge.start_vertex().clone(),
diff --git a/crates/fj-core/src/operations/reverse/cycle.rs b/crates/fj-core/src/operations/reverse/cycle.rs
index a8985ba68..f3d12acff 100644
--- a/crates/fj-core/src/operations/reverse/cycle.rs
+++ b/crates/fj-core/src/operations/reverse/cycle.rs
@@ -31,11 +31,10 @@ impl Reverse for Cycle {
 
 impl ReverseCurveCoordinateSystems for Cycle {
     fn reverse_curve_coordinate_systems(&self, core: &mut Core) -> Self {
-        let edges = self.half_edges().iter().map(|edge| {
-            edge.reverse_curve_coordinate_systems(core)
-                .insert(core)
-                .derive_from(edge, core)
-        });
+        let edges = self
+            .half_edges()
+            .iter()
+            .map(|edge| edge.reverse_curve_coordinate_systems(core));
 
         Cycle::new(edges)
     }
diff --git a/crates/fj-core/src/operations/reverse/edge.rs b/crates/fj-core/src/operations/reverse/edge.rs
index e58f7c7b3..91e6affa2 100644
--- a/crates/fj-core/src/operations/reverse/edge.rs
+++ b/crates/fj-core/src/operations/reverse/edge.rs
@@ -1,9 +1,14 @@
-use crate::{objects::HalfEdge, Core};
+use crate::{
+    objects::HalfEdge,
+    operations::{derive::DeriveFrom, insert::Insert},
+    storage::Handle,
+    Core,
+};
 
 use super::ReverseCurveCoordinateSystems;
 
-impl ReverseCurveCoordinateSystems for HalfEdge {
-    fn reverse_curve_coordinate_systems(&self, _: &mut Core) -> Self {
+impl ReverseCurveCoordinateSystems for Handle<HalfEdge> {
+    fn reverse_curve_coordinate_systems(&self, core: &mut Core) -> Self {
         let path = self.path().reverse();
         let boundary = self.boundary().reverse();
 
@@ -13,5 +18,7 @@ impl ReverseCurveCoordinateSystems for HalfEdge {
             self.curve().clone(),
             self.start_vertex().clone(),
         )
+        .insert(core)
+        .derive_from(self, core)
     }
 }
diff --git a/crates/fj-core/src/operations/split/edge.rs b/crates/fj-core/src/operations/split/edge.rs
index 2a74412d1..fd476bcb5 100644
--- a/crates/fj-core/src/operations/split/edge.rs
+++ b/crates/fj-core/src/operations/split/edge.rs
@@ -48,10 +48,12 @@ impl SplitEdge for Shell {
 
         let siblings = {
             let [sibling_a, sibling_b] = sibling.split_half_edge(point, core);
-            let sibling_b = sibling_b.update_start_vertex(
-                |_, _| half_edge_b.start_vertex().clone(),
-                core,
-            );
+            let sibling_b = sibling_b
+                .update_start_vertex(
+                    |_, _| half_edge_b.start_vertex().clone(),
+                    core,
+                )
+                .insert(core);
             [sibling_a, sibling_b].map(|half_edge| {
                 half_edge.insert(core).derive_from(&sibling, core)
             })
diff --git a/crates/fj-core/src/operations/split/face.rs b/crates/fj-core/src/operations/split/face.rs
index e455b7de4..11a7bf513 100644
--- a/crates/fj-core/src/operations/split/face.rs
+++ b/crates/fj-core/src/operations/split/face.rs
@@ -106,10 +106,12 @@ impl SplitFace for Shell {
             None,
             core,
         )
-        .update_start_vertex(|_, _| b.start_vertex().clone(), core);
+        .update_start_vertex(|_, _| b.start_vertex().clone(), core)
+        .insert(core);
         let dividing_half_edge_c_to_b = HalfEdge::from_sibling(
             &dividing_half_edge_a_to_d,
             d.start_vertex().clone(),
+            core,
         );
 
         let mut half_edges_of_face_starting_at_b =
diff --git a/crates/fj-core/src/operations/split/half_edge.rs b/crates/fj-core/src/operations/split/half_edge.rs
index cb2d0d8e5..d842fae1e 100644
--- a/crates/fj-core/src/operations/split/half_edge.rs
+++ b/crates/fj-core/src/operations/split/half_edge.rs
@@ -3,6 +3,7 @@ use fj_math::Point;
 use crate::{
     objects::{HalfEdge, Vertex},
     operations::insert::Insert,
+    storage::Handle,
     Core,
 };
 
@@ -28,7 +29,7 @@ pub trait SplitHalfEdge {
         &self,
         point: impl Into<Point<1>>,
         core: &mut Core,
-    ) -> [HalfEdge; 2];
+    ) -> [Handle<HalfEdge>; 2];
 }
 
 impl SplitHalfEdge for HalfEdge {
@@ -36,7 +37,7 @@ impl SplitHalfEdge for HalfEdge {
         &self,
         point: impl Into<Point<1>>,
         core: &mut Core,
-    ) -> [HalfEdge; 2] {
+    ) -> [Handle<HalfEdge>; 2] {
         let point = point.into();
 
         let [start, end] = self.boundary().inner;
@@ -46,13 +47,15 @@ impl SplitHalfEdge for HalfEdge {
             [start, point],
             self.curve().clone(),
             self.start_vertex().clone(),
-        );
+        )
+        .insert(core);
         let b = HalfEdge::new(
             self.path(),
             [point, end],
             self.curve().clone(),
             Vertex::new().insert(core),
-        );
+        )
+        .insert(core);
 
         [a, b]
     }
diff --git a/crates/fj-core/src/operations/transform/edge.rs b/crates/fj-core/src/operations/transform/edge.rs
index 5aa5424f1..9c11a244d 100644
--- a/crates/fj-core/src/operations/transform/edge.rs
+++ b/crates/fj-core/src/operations/transform/edge.rs
@@ -1,10 +1,12 @@
 use fj_math::Transform;
 
-use crate::{objects::HalfEdge, Core};
+use crate::{
+    objects::HalfEdge, operations::insert::Insert, storage::Handle, Core,
+};
 
 use super::{TransformCache, TransformObject};
 
-impl TransformObject for HalfEdge {
+impl TransformObject for Handle<HalfEdge> {
     fn transform_with_cache(
         &self,
         transform: &Transform,
@@ -24,6 +26,6 @@ impl TransformObject for HalfEdge {
             .clone()
             .transform_with_cache(transform, core, cache);
 
-        Self::new(path, boundary, curve, start_vertex)
+        HalfEdge::new(path, boundary, curve, start_vertex).insert(core)
     }
 }
diff --git a/crates/fj-core/src/operations/update/half_edge.rs b/crates/fj-core/src/operations/update/half_edge.rs
index ef7dbf9e9..c8992c629 100644
--- a/crates/fj-core/src/operations/update/half_edge.rs
+++ b/crates/fj-core/src/operations/update/half_edge.rs
@@ -9,13 +9,14 @@ use crate::{
 };
 
 /// Update a [`HalfEdge`]
-pub trait UpdateHalfEdge {
+pub trait UpdateHalfEdge: Sized {
     /// Update the path of the edge
     #[must_use]
     fn update_path(
         &self,
         update: impl FnOnce(SurfacePath) -> SurfacePath,
-    ) -> Self;
+        core: &mut Core,
+    ) -> Handle<Self>;
 
     /// Update the boundary of the edge
     #[must_use]
@@ -49,13 +50,17 @@ impl UpdateHalfEdge for HalfEdge {
     fn update_path(
         &self,
         update: impl FnOnce(SurfacePath) -> SurfacePath,
-    ) -> Self {
+        core: &mut Core,
+    ) -> Handle<Self> {
+        let path = update(self.path());
+
         HalfEdge::new(
-            update(self.path()),
+            path,
             self.boundary(),
             self.curve().clone(),
             self.start_vertex().clone(),
         )
+        .insert(core)
     }
 
     fn update_boundary(
diff --git a/crates/fj-core/src/validate/shell.rs b/crates/fj-core/src/validate/shell.rs
index 2628a30f7..ff062f243 100644
--- a/crates/fj-core/src/validate/shell.rs
+++ b/crates/fj-core/src/validate/shell.rs
@@ -429,9 +429,12 @@ mod tests {
                             |cycle, core| {
                                 cycle.update_half_edge(
                                     cycle.half_edges().nth_circular(0),
-                                    |edge, _| {
+                                    |edge, core| {
                                         [edge
-                                            .update_path(|path| path.reverse())
+                                            .update_path(
+                                                |path| path.reverse(),
+                                                core,
+                                            )
                                             .update_boundary(|boundary| {
                                                 boundary.reverse()
                                             })]
diff --git a/crates/fj-core/src/validate/sketch.rs b/crates/fj-core/src/validate/sketch.rs
index 2674a177d..100ed5fa8 100644
--- a/crates/fj-core/src/validate/sketch.rs
+++ b/crates/fj-core/src/validate/sketch.rs
@@ -186,8 +186,7 @@ mod tests {
     fn should_find_clockwise_exterior_cycle() -> anyhow::Result<()> {
         let mut core = Core::new();
 
-        let valid_outer_circle =
-            HalfEdge::circle([0., 0.], 1., &mut core).insert(&mut core);
+        let valid_outer_circle = HalfEdge::circle([0., 0.], 1., &mut core);
         let valid_exterior =
             Cycle::new(vec![valid_outer_circle.clone()]).insert(&mut core);
         let valid_sketch =
@@ -199,8 +198,8 @@ mod tests {
         let invalid_outer_circle = HalfEdge::from_sibling(
             &valid_outer_circle,
             Vertex::new().insert(&mut core),
-        )
-        .insert(&mut core);
+            &mut core,
+        );
         let invalid_exterior =
             Cycle::new(vec![invalid_outer_circle.clone()]).insert(&mut core);
         let invalid_sketch =
@@ -222,15 +221,13 @@ mod tests {
     fn should_find_counterclockwise_interior_cycle() -> anyhow::Result<()> {
         let mut core = Core::new();
 
-        let outer_circle =
-            HalfEdge::circle([0., 0.], 2., &mut core).insert(&mut core);
-        let inner_circle =
-            HalfEdge::circle([0., 0.], 1., &mut core).insert(&mut core);
+        let outer_circle = HalfEdge::circle([0., 0.], 2., &mut core);
+        let inner_circle = HalfEdge::circle([0., 0.], 1., &mut core);
         let cw_inner_circle = HalfEdge::from_sibling(
             &inner_circle,
             Vertex::new().insert(&mut core),
-        )
-        .insert(&mut core);
+            &mut core,
+        );
         let exterior = Cycle::new(vec![outer_circle.clone()]).insert(&mut core);
 
         let valid_interior =
diff --git a/crates/fj-core/src/validate/solid.rs b/crates/fj-core/src/validate/solid.rs
index 60df5825b..394fe750e 100644
--- a/crates/fj-core/src/validate/solid.rs
+++ b/crates/fj-core/src/validate/solid.rs
@@ -202,10 +202,8 @@ mod tests {
                 &mut core,
             ),
             Region::new(
-                Cycle::new(vec![
-                    HalfEdge::circle([0., 0.], 1., &mut core).insert(&mut core)
-                ])
-                .insert(&mut core),
+                Cycle::new(vec![HalfEdge::circle([0., 0.], 1., &mut core)])
+                    .insert(&mut core),
                 vec![],
             )
             .insert(&mut core),
@@ -249,10 +247,8 @@ mod tests {
         let mut core = Core::new();
 
         let shared_region = Region::new(
-            Cycle::new(vec![
-                HalfEdge::circle([0., 0.], 1., &mut core).insert(&mut core)
-            ])
-            .insert(&mut core),
+            Cycle::new(vec![HalfEdge::circle([0., 0.], 1., &mut core)])
+                .insert(&mut core),
             vec![],
         )
         .insert(&mut core);
@@ -302,10 +298,8 @@ mod tests {
         let mut core = Core::new();
 
         let shared_cycle =
-            Cycle::new(vec![
-                HalfEdge::circle([0., 0.], 1., &mut core).insert(&mut core)
-            ])
-            .insert(&mut core);
+            Cycle::new(vec![HalfEdge::circle([0., 0.], 1., &mut core)])
+                .insert(&mut core);
 
         let invalid_solid = Solid::new(vec![Shell::new(vec![
             Face::new(
@@ -351,8 +345,7 @@ mod tests {
     fn should_find_half_edge_multiple_references() -> anyhow::Result<()> {
         let mut core = Core::new();
 
-        let shared_edge =
-            HalfEdge::circle([0., 0.], 1., &mut core).insert(&mut core);
+        let shared_edge = HalfEdge::circle([0., 0.], 1., &mut core);
 
         let invalid_solid = Solid::new(vec![Shell::new(vec![Face::new(
             Surface::surface_from_uv(