diff --git a/crates/fj-core/src/algorithms/mod.rs b/crates/fj-core/src/algorithms/mod.rs
index 4c5f9ad38..6665e8ba5 100644
--- a/crates/fj-core/src/algorithms/mod.rs
+++ b/crates/fj-core/src/algorithms/mod.rs
@@ -13,6 +13,5 @@
 pub mod approx;
 pub mod bounding_volume;
 pub mod intersect;
-pub mod sweep;
 pub mod transform;
 pub mod triangulate;
diff --git a/crates/fj-core/src/operations/mod.rs b/crates/fj-core/src/operations/mod.rs
index ea218d6dd..405884c50 100644
--- a/crates/fj-core/src/operations/mod.rs
+++ b/crates/fj-core/src/operations/mod.rs
@@ -45,4 +45,5 @@ pub mod merge;
 pub mod replace;
 pub mod reverse;
 pub mod split;
+pub mod sweep;
 pub mod update;
diff --git a/crates/fj-core/src/algorithms/sweep/face.rs b/crates/fj-core/src/operations/sweep/face.rs
similarity index 88%
rename from crates/fj-core/src/algorithms/sweep/face.rs
rename to crates/fj-core/src/operations/sweep/face.rs
index a08a5cb2c..46ac6f3c3 100644
--- a/crates/fj-core/src/algorithms/sweep/face.rs
+++ b/crates/fj-core/src/operations/sweep/face.rs
@@ -10,13 +10,12 @@ use crate::{
         build::BuildCycle, insert::Insert, join::JoinCycle, reverse::Reverse,
     },
     services::Services,
-    storage::Handle,
 };
 
 use super::{Sweep, SweepCache};
 
-impl Sweep for Handle<Face> {
-    type Swept = Handle<Shell>;
+impl Sweep for &Face {
+    type Swept = Shell;
 
     fn sweep_with_cache(
         self,
@@ -41,7 +40,7 @@ impl Sweep for Handle<Face> {
 
         let mut faces = Vec::new();
 
-        let bottom_face = bottom_face(self, path, services);
+        let bottom_face = bottom_face(self, path, services).insert(services);
         faces.push(bottom_face.clone());
 
         let top_surface =
@@ -65,12 +64,14 @@ impl Sweep for Handle<Face> {
 
                 let (side_face, top_edge) = (
                     bottom_half_edge.deref(),
-                    bottom_half_edge_next.start_vertex(),
+                    bottom_half_edge_next.start_vertex().clone(),
                     bottom_face.surface().deref(),
                     bottom_face.region().color(),
                 )
                     .sweep_with_cache(path, cache, services);
 
+                let side_face = side_face.insert(services);
+
                 faces.push(side_face);
 
                 top_edges.push((
@@ -101,19 +102,15 @@ impl Sweep for Handle<Face> {
         let top_face = Face::new(top_surface, top_region).insert(services);
         faces.push(top_face);
 
-        Shell::new(faces).insert(services)
+        Shell::new(faces)
     }
 }
 
-fn bottom_face(
-    face: Handle<Face>,
-    path: Vector<3>,
-    services: &mut Services,
-) -> Handle<Face> {
+fn bottom_face(face: &Face, path: Vector<3>, services: &mut Services) -> Face {
     let is_negative_sweep = {
         let u = match face.surface().geometry().u {
             GlobalPath::Circle(_) => todo!(
-                "Sweeping from faces defined in round surfaces is not \
+                "Sweeping from faces defined in rounded surfaces is not \
                     supported"
             ),
             GlobalPath::Line(line) => line.direction(),
@@ -126,8 +123,8 @@ fn bottom_face(
     };
 
     if is_negative_sweep {
-        face
+        face.clone()
     } else {
-        face.reverse(services).insert(services)
+        face.reverse(services)
     }
 }
diff --git a/crates/fj-core/src/algorithms/sweep/edge.rs b/crates/fj-core/src/operations/sweep/half_edge.rs
similarity index 76%
rename from crates/fj-core/src/algorithms/sweep/edge.rs
rename to crates/fj-core/src/operations/sweep/half_edge.rs
index fe227d26a..81c92b83d 100644
--- a/crates/fj-core/src/algorithms/sweep/edge.rs
+++ b/crates/fj-core/src/operations/sweep/half_edge.rs
@@ -4,7 +4,7 @@ use fj_math::{Point, Scalar, Vector};
 use crate::{
     objects::{Cycle, Face, HalfEdge, Region, Surface, Vertex},
     operations::{
-        build::BuildHalfEdge,
+        build::{BuildCycle, BuildHalfEdge},
         insert::Insert,
         update::{UpdateCycle, UpdateHalfEdge},
     },
@@ -14,8 +14,8 @@ use crate::{
 
 use super::{Sweep, SweepCache};
 
-impl Sweep for (&HalfEdge, &Handle<Vertex>, &Surface, Option<Color>) {
-    type Swept = (Handle<Face>, Handle<HalfEdge>);
+impl Sweep for (&HalfEdge, Handle<Vertex>, &Surface, Option<Color>) {
+    type Swept = (Face, Handle<HalfEdge>);
 
     fn sweep_with_cache(
         self,
@@ -23,19 +23,20 @@ impl Sweep for (&HalfEdge, &Handle<Vertex>, &Surface, Option<Color>) {
         cache: &mut SweepCache,
         services: &mut Services,
     ) -> Self::Swept {
-        let (edge, next_vertex, surface, color) = self;
+        let (edge, end_vertex, surface, color) = self;
         let path = path.into();
 
-        let surface =
-            (edge.path(), surface).sweep_with_cache(path, cache, services);
+        let surface = (edge.path(), surface)
+            .sweep_with_cache(path, cache, services)
+            .insert(services);
 
         // Next, we need to define the boundaries of the face. Let's start with
         // the global vertices and edges.
         let (vertices, curves) = {
-            let [a, b] = [edge.start_vertex(), next_vertex].map(Clone::clone);
-            let (curve_up, [_, c]) =
+            let [a, b] = [edge.start_vertex().clone(), end_vertex];
+            let (curve_up, c) =
                 b.clone().sweep_with_cache(path, cache, services);
-            let (curve_down, [_, d]) =
+            let (curve_down, d) =
                 a.clone().sweep_with_cache(path, cache, services);
 
             (
@@ -75,7 +76,7 @@ impl Sweep for (&HalfEdge, &Handle<Vertex>, &Surface, Option<Color>) {
             [[a, b], [c, d], [b, a], [d, c]]
         };
 
-        let mut exterior = Some(Cycle::new([]));
+        let mut exterior = Cycle::empty();
 
         // Armed with all of that, we're ready to create the edges.
         let [_edge_bottom, _edge_up, edge_top, _edge_down] = boundaries
@@ -101,21 +102,15 @@ impl Sweep for (&HalfEdge, &Handle<Vertex>, &Surface, Option<Color>) {
                     edge.insert(services)
                 };
 
-                exterior = Some(
-                    exterior.take().unwrap().add_half_edges([edge.clone()]),
-                );
+                exterior = exterior.add_half_edges([edge.clone()]);
 
                 edge
             });
 
-        let region = Region::new(exterior.unwrap().insert(services), [], color)
-            .insert(services);
-
+        let exterior = exterior.insert(services);
+        let region = Region::new(exterior, [], color).insert(services);
         let face = Face::new(surface, region);
 
-        // And we're done creating the face! All that's left to do is build our
-        // return values.
-        let face = face.insert(services);
         (face, edge_top)
     }
 }
diff --git a/crates/fj-core/src/algorithms/sweep/mod.rs b/crates/fj-core/src/operations/sweep/mod.rs
similarity index 98%
rename from crates/fj-core/src/algorithms/sweep/mod.rs
rename to crates/fj-core/src/operations/sweep/mod.rs
index 04d808895..434379648 100644
--- a/crates/fj-core/src/algorithms/sweep/mod.rs
+++ b/crates/fj-core/src/operations/sweep/mod.rs
@@ -1,7 +1,7 @@
 //! Sweeping objects along a path to create new objects
 
-mod edge;
 mod face;
+mod half_edge;
 mod path;
 mod sketch;
 mod vertex;
diff --git a/crates/fj-core/src/algorithms/sweep/path.rs b/crates/fj-core/src/operations/sweep/path.rs
similarity index 92%
rename from crates/fj-core/src/algorithms/sweep/path.rs
rename to crates/fj-core/src/operations/sweep/path.rs
index 2e1fc85e3..cb5caab04 100644
--- a/crates/fj-core/src/algorithms/sweep/path.rs
+++ b/crates/fj-core/src/operations/sweep/path.rs
@@ -3,21 +3,19 @@ use fj_math::{Circle, Line, Vector};
 use crate::{
     geometry::{GlobalPath, SurfaceGeometry, SurfacePath},
     objects::Surface,
-    operations::insert::Insert,
     services::Services,
-    storage::Handle,
 };
 
 use super::{Sweep, SweepCache};
 
 impl Sweep for (SurfacePath, &Surface) {
-    type Swept = Handle<Surface>;
+    type Swept = Surface;
 
     fn sweep_with_cache(
         self,
         path: impl Into<Vector<3>>,
         _: &mut SweepCache,
-        services: &mut Services,
+        _: &mut Services,
     ) -> Self::Swept {
         let (curve, surface) = self;
 
@@ -72,6 +70,6 @@ impl Sweep for (SurfacePath, &Surface) {
             }
         };
 
-        Surface::new(SurfaceGeometry { u, v: path.into() }).insert(services)
+        Surface::new(SurfaceGeometry { u, v: path.into() })
     }
 }
diff --git a/crates/fj-core/src/algorithms/sweep/sketch.rs b/crates/fj-core/src/operations/sweep/sketch.rs
similarity index 75%
rename from crates/fj-core/src/algorithms/sweep/sketch.rs
rename to crates/fj-core/src/operations/sweep/sketch.rs
index bf0e555b3..f5cde015d 100644
--- a/crates/fj-core/src/algorithms/sweep/sketch.rs
+++ b/crates/fj-core/src/operations/sweep/sketch.rs
@@ -9,8 +9,8 @@ use crate::{
 
 use super::{Sweep, SweepCache};
 
-impl Sweep for (Handle<Sketch>, Handle<Surface>) {
-    type Swept = Handle<Solid>;
+impl Sweep for (&Sketch, Handle<Surface>) {
+    type Swept = Solid;
 
     fn sweep_with_cache(
         self,
@@ -25,10 +25,12 @@ impl Sweep for (Handle<Sketch>, Handle<Surface>) {
         for region in sketch.regions() {
             let face =
                 Face::new(surface.clone(), region.clone()).insert(services);
-            let shell = face.sweep_with_cache(path, cache, services);
+            let shell = face
+                .sweep_with_cache(path, cache, services)
+                .insert(services);
             shells.push(shell);
         }
 
-        Solid::new(shells).insert(services)
+        Solid::new(shells)
     }
 }
diff --git a/crates/fj-core/src/algorithms/sweep/vertex.rs b/crates/fj-core/src/operations/sweep/vertex.rs
similarity index 81%
rename from crates/fj-core/src/algorithms/sweep/vertex.rs
rename to crates/fj-core/src/operations/sweep/vertex.rs
index 603583ffe..f998d5907 100644
--- a/crates/fj-core/src/algorithms/sweep/vertex.rs
+++ b/crates/fj-core/src/operations/sweep/vertex.rs
@@ -10,7 +10,7 @@ use crate::{
 use super::{Sweep, SweepCache};
 
 impl Sweep for Handle<Vertex> {
-    type Swept = (Handle<Curve>, [Self; 2]);
+    type Swept = (Handle<Curve>, Self);
 
     fn sweep_with_cache(
         self,
@@ -24,14 +24,12 @@ impl Sweep for Handle<Vertex> {
             .or_insert_with(|| Curve::new().insert(services))
             .clone();
 
-        let a = self.clone();
-        let b = cache
+        let vertex = cache
             .vertices
             .entry(self.id())
             .or_insert_with(|| Vertex::new().insert(services))
             .clone();
-        let vertices = [a, b];
 
-        (curve, vertices)
+        (curve, vertex)
     }
 }
diff --git a/models/cuboid/src/lib.rs b/models/cuboid/src/lib.rs
index 8588c2b22..2f6dcf305 100644
--- a/models/cuboid/src/lib.rs
+++ b/models/cuboid/src/lib.rs
@@ -1,10 +1,10 @@
 use fj::{
     core::{
-        algorithms::sweep::Sweep,
         objects::{Region, Sketch, Solid},
         operations::{
             build::{BuildRegion, BuildSketch},
             insert::Insert,
+            sweep::Sweep,
             update::UpdateSketch,
         },
         services::Services,
@@ -14,22 +14,20 @@ use fj::{
 };
 
 pub fn model(x: f64, y: f64, z: f64, services: &mut Services) -> Handle<Solid> {
-    let sketch = Sketch::empty()
-        .add_region(
-            Region::polygon(
-                [
-                    [-x / 2., -y / 2.],
-                    [x / 2., -y / 2.],
-                    [x / 2., y / 2.],
-                    [-x / 2., y / 2.],
-                ],
-                services,
-            )
-            .insert(services),
+    let sketch = Sketch::empty().add_region(
+        Region::polygon(
+            [
+                [-x / 2., -y / 2.],
+                [x / 2., -y / 2.],
+                [x / 2., y / 2.],
+                [-x / 2., y / 2.],
+            ],
+            services,
         )
-        .insert(services);
+        .insert(services),
+    );
 
     let surface = services.objects.surfaces.xy_plane();
     let path = Vector::from([0., 0., z]);
-    (sketch, surface).sweep(path, services)
+    (&sketch, surface).sweep(path, services).insert(services)
 }
diff --git a/models/spacer/src/lib.rs b/models/spacer/src/lib.rs
index 253a2fc64..586bf0c4b 100644
--- a/models/spacer/src/lib.rs
+++ b/models/spacer/src/lib.rs
@@ -1,11 +1,11 @@
 use fj::{
     core::{
-        algorithms::sweep::Sweep,
         objects::{Cycle, Region, Sketch, Solid},
         operations::{
             build::{BuildCycle, BuildRegion, BuildSketch},
             insert::Insert,
             reverse::Reverse,
+            sweep::Sweep,
             update::{UpdateRegion, UpdateSketch},
         },
         services::Services,
@@ -20,21 +20,15 @@ pub fn model(
     height: f64,
     services: &mut Services,
 ) -> Handle<Solid> {
-    let sketch = Sketch::empty()
-        .add_region(
-            Region::circle(Point::origin(), outer, services)
-                .add_interiors([Cycle::circle(
-                    Point::origin(),
-                    inner,
-                    services,
-                )
+    let sketch = Sketch::empty().add_region(
+        Region::circle(Point::origin(), outer, services)
+            .add_interiors([Cycle::circle(Point::origin(), inner, services)
                 .reverse(services)
                 .insert(services)])
-                .insert(services),
-        )
-        .insert(services);
+            .insert(services),
+    );
 
     let surface = services.objects.surfaces.xy_plane();
     let path = Vector::from([0., 0., height]);
-    (sketch, surface).sweep(path, services)
+    (&sketch, surface).sweep(path, services).insert(services)
 }
diff --git a/models/split/src/lib.rs b/models/split/src/lib.rs
index f3d7c19ad..3cbdaec53 100644
--- a/models/split/src/lib.rs
+++ b/models/split/src/lib.rs
@@ -1,11 +1,11 @@
 use fj::{
     core::{
-        algorithms::sweep::Sweep,
         objects::{Region, Sketch, Solid},
         operations::{
             build::{BuildRegion, BuildSketch},
             insert::Insert,
             split::SplitFace,
+            sweep::Sweep,
             update::{UpdateSketch, UpdateSolid},
         },
         services::Services,
@@ -19,24 +19,22 @@ pub fn model(
     split_pos: f64,
     services: &mut Services,
 ) -> Handle<Solid> {
-    let sketch = Sketch::empty()
-        .add_region(
-            Region::polygon(
-                [
-                    [-size / 2., -size / 2.],
-                    [size / 2., -size / 2.],
-                    [size / 2., size / 2.],
-                    [-size / 2., size / 2.],
-                ],
-                services,
-            )
-            .insert(services),
+    let sketch = Sketch::empty().add_region(
+        Region::polygon(
+            [
+                [-size / 2., -size / 2.],
+                [size / 2., -size / 2.],
+                [size / 2., size / 2.],
+                [-size / 2., size / 2.],
+            ],
+            services,
         )
-        .insert(services);
+        .insert(services),
+    );
 
     let surface = services.objects.surfaces.xy_plane();
     let path = Vector::from([0., 0., size]);
-    let solid = (sketch, surface).sweep(path, services);
+    let solid = (&sketch, surface).sweep(path, services);
 
     solid
         .update_shell(solid.shells().only(), |shell| {
diff --git a/models/star/src/lib.rs b/models/star/src/lib.rs
index c6ce938c0..b46e7b862 100644
--- a/models/star/src/lib.rs
+++ b/models/star/src/lib.rs
@@ -2,12 +2,12 @@ use std::f64::consts::PI;
 
 use fj::{
     core::{
-        algorithms::sweep::Sweep,
         objects::{Cycle, Region, Sketch, Solid},
         operations::{
             build::{BuildCycle, BuildRegion, BuildSketch},
             insert::Insert,
             reverse::Reverse,
+            sweep::Sweep,
             update::{UpdateRegion, UpdateSketch},
         },
         services::Services,
@@ -43,17 +43,15 @@ pub fn model(
         inner_points.push([x / 2., y / 2.]);
     }
 
-    let sketch = Sketch::empty()
-        .add_region(
-            Region::polygon(outer_points, services)
-                .add_interiors([Cycle::polygon(inner_points, services)
-                    .reverse(services)
-                    .insert(services)])
-                .insert(services),
-        )
-        .insert(services);
+    let sketch = Sketch::empty().add_region(
+        Region::polygon(outer_points, services)
+            .add_interiors([Cycle::polygon(inner_points, services)
+                .reverse(services)
+                .insert(services)])
+            .insert(services),
+    );
 
     let surface = services.objects.surfaces.xy_plane();
     let path = Vector::from([0., 0., h]);
-    (sketch, surface).sweep(path, services)
+    (&sketch, surface).sweep(path, services).insert(services)
 }