diff --git a/crates/fj-kernel/src/algorithms/approx/curve.rs b/crates/fj-kernel/src/algorithms/approx/curve.rs
index 2f06121a04..16f9e26e4f 100644
--- a/crates/fj-kernel/src/algorithms/approx/curve.rs
+++ b/crates/fj-kernel/src/algorithms/approx/curve.rs
@@ -198,6 +198,7 @@ mod tests {
     use crate::{
         algorithms::approx::{path::RangeOnPath, Approx, ApproxPoint},
         builder::CurveBuilder,
+        insert::Insert,
         objects::{Curve, Objects, Surface},
         partial::HasPartial,
         path::GlobalPath,
@@ -215,7 +216,8 @@ mod tests {
         let curve = Curve::partial()
             .with_surface(Some(surface))
             .update_as_line_from_points([[1., 1.], [2., 1.]])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
         let range = RangeOnPath::from([[0.], [1.]]);
 
         let approx = (&curve, range).approx(1.);
@@ -236,7 +238,8 @@ mod tests {
         let curve = Curve::partial()
             .with_surface(Some(surface))
             .update_as_line_from_points([[1., 1.], [1., 2.]])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
         let range = RangeOnPath::from([[0.], [1.]]);
 
         let approx = (&curve, range).approx(1.);
@@ -255,7 +258,8 @@ mod tests {
         let curve = Curve::partial()
             .with_surface(Some(surface.clone()))
             .update_as_line_from_points([[0., 1.], [1., 1.]])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
 
         let range = RangeOnPath::from([[0.], [TAU]]);
         let tolerance = 1.;
@@ -287,7 +291,8 @@ mod tests {
         let curve = Curve::partial()
             .with_surface(Some(surface))
             .update_as_circle_from_radius(1.)
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
 
         let range = RangeOnPath::from([[0.], [TAU]]);
         let tolerance = 1.;
diff --git a/crates/fj-kernel/src/algorithms/intersect/face_face.rs b/crates/fj-kernel/src/algorithms/intersect/face_face.rs
index 66b41ac301..9207a208e3 100644
--- a/crates/fj-kernel/src/algorithms/intersect/face_face.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/face_face.rs
@@ -68,8 +68,10 @@ mod tests {
     use crate::{
         algorithms::intersect::CurveFaceIntersection,
         builder::{CurveBuilder, FaceBuilder},
+        insert::Insert,
         objects::{Curve, Face, Objects},
         partial::HasPartial,
+        validate::ValidationError,
     };
 
     use super::FaceFaceIntersection;
@@ -122,12 +124,14 @@ mod tests {
 
         let intersection = FaceFaceIntersection::compute([&a, &b], &objects)?;
 
-        let expected_curves = surfaces.try_map_ext(|surface| {
-            Curve::partial()
-                .with_surface(Some(surface))
-                .update_as_line_from_points([[0., 0.], [1., 0.]])
-                .build(&objects)
-        })?;
+        let expected_curves =
+            surfaces.try_map_ext(|surface| -> Result<_, ValidationError> {
+                Ok(Curve::partial()
+                    .with_surface(Some(surface))
+                    .update_as_line_from_points([[0., 0.], [1., 0.]])
+                    .build(&objects)?
+                    .insert(&objects)?)
+            })?;
         let expected_intervals =
             CurveFaceIntersection::from_intervals([[[-1.], [1.]]]);
         assert_eq!(
diff --git a/crates/fj-kernel/src/algorithms/intersect/face_point.rs b/crates/fj-kernel/src/algorithms/intersect/face_point.rs
index 6fa3d17b90..22c50b3f8e 100644
--- a/crates/fj-kernel/src/algorithms/intersect/face_point.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/face_point.rs
@@ -137,6 +137,7 @@ mod tests {
     use crate::{
         algorithms::intersect::{face_point::FacePointIntersection, Intersect},
         builder::FaceBuilder,
+        insert::Insert,
         iter::ObjectIters,
         objects::{Face, Objects},
         partial::HasPartial,
@@ -150,7 +151,8 @@ mod tests {
         let face = Face::partial()
             .with_surface(surface)
             .with_exterior_polygon_from_points([[0., 0.], [1., 1.], [0., 2.]])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
         let point = Point::from([2., 1.]);
 
         let intersection = (&face, &point).intersect();
@@ -167,7 +169,8 @@ mod tests {
         let face = Face::partial()
             .with_surface(surface)
             .with_exterior_polygon_from_points([[0., 0.], [2., 1.], [0., 2.]])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
         let point = Point::from([1., 1.]);
 
         let intersection = (&face, &point).intersect();
@@ -187,7 +190,8 @@ mod tests {
         let face = Face::partial()
             .with_surface(surface)
             .with_exterior_polygon_from_points([[4., 2.], [0., 4.], [0., 0.]])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
         let point = Point::from([1., 2.]);
 
         let intersection = (&face, &point).intersect();
@@ -212,7 +216,8 @@ mod tests {
                 [3., 0.],
                 [3., 4.],
             ])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
         let point = Point::from([1., 1.]);
 
         let intersection = (&face, &point).intersect();
@@ -238,7 +243,8 @@ mod tests {
                 [3., 1.],
                 [0., 2.],
             ])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
         let point = Point::from([1., 1.]);
 
         let intersection = (&face, &point).intersect();
@@ -265,7 +271,8 @@ mod tests {
                 [4., 0.],
                 [4., 5.],
             ])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
         let point = Point::from([1., 1.]);
 
         let intersection = (&face, &point).intersect();
@@ -285,7 +292,8 @@ mod tests {
         let face = Face::partial()
             .with_surface(surface)
             .with_exterior_polygon_from_points([[0., 0.], [2., 0.], [0., 1.]])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
         let point = Point::from([1., 0.]);
 
         let intersection = (&face, &point).intersect();
@@ -314,7 +322,8 @@ mod tests {
         let face = Face::partial()
             .with_surface(surface)
             .with_exterior_polygon_from_points([[0., 0.], [1., 0.], [0., 1.]])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
         let point = Point::from([1., 0.]);
 
         let intersection = (&face, &point).intersect();
diff --git a/crates/fj-kernel/src/algorithms/intersect/ray_face.rs b/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
index 38201c3720..f5526972f0 100644
--- a/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/ray_face.rs
@@ -153,6 +153,7 @@ mod tests {
             transform::TransformObject,
         },
         builder::FaceBuilder,
+        insert::Insert,
         iter::ObjectIters,
         objects::{Face, Objects},
         partial::HasPartial,
@@ -174,6 +175,7 @@ mod tests {
                 [-1., 1.],
             ])
             .build(&objects)?
+            .insert(&objects)?
             .translate([-1., 0., 0.], &objects)?;
 
         assert_eq!((&ray, &face).intersect(), None);
@@ -196,6 +198,7 @@ mod tests {
                 [-1., 1.],
             ])
             .build(&objects)?
+            .insert(&objects)?
             .translate([1., 0., 0.], &objects)?;
 
         assert_eq!(
@@ -221,6 +224,7 @@ mod tests {
                 [-1., 1.],
             ])
             .build(&objects)?
+            .insert(&objects)?
             .translate([0., 0., 2.], &objects)?;
 
         assert_eq!((&ray, &face).intersect(), None);
@@ -243,6 +247,7 @@ mod tests {
                 [-1., 1.],
             ])
             .build(&objects)?
+            .insert(&objects)?
             .translate([1., 1., 0.], &objects)?;
 
         let edge = face
@@ -276,6 +281,7 @@ mod tests {
                 [-1., 1.],
             ])
             .build(&objects)?
+            .insert(&objects)?
             .translate([1., 1., 1.], &objects)?;
 
         let vertex = face
@@ -306,7 +312,8 @@ mod tests {
                 [1., 1.],
                 [-1., 1.],
             ])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
 
         assert_eq!(
             (&ray, &face).intersect(),
@@ -332,6 +339,7 @@ mod tests {
                 [-1., 1.],
             ])
             .build(&objects)?
+            .insert(&objects)?
             .translate([0., 0., 1.], &objects)?;
 
         assert_eq!((&ray, &face).intersect(), None);
diff --git a/crates/fj-kernel/src/algorithms/intersect/surface_surface.rs b/crates/fj-kernel/src/algorithms/intersect/surface_surface.rs
index 869e7cc4a0..7481608f93 100644
--- a/crates/fj-kernel/src/algorithms/intersect/surface_surface.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/surface_surface.rs
@@ -93,6 +93,7 @@ mod tests {
     use crate::{
         algorithms::transform::TransformObject,
         builder::CurveBuilder,
+        insert::Insert,
         objects::{Curve, Objects},
         partial::HasPartial,
     };
@@ -124,11 +125,13 @@ mod tests {
         let expected_xy = Curve::partial()
             .with_surface(Some(xy.clone()))
             .update_as_u_axis()
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
         let expected_xz = Curve::partial()
             .with_surface(Some(xz.clone()))
             .update_as_u_axis()
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
 
         assert_eq!(
             SurfaceSurfaceIntersection::compute([xy, xz], &objects)?,
diff --git a/crates/fj-kernel/src/algorithms/reverse/face.rs b/crates/fj-kernel/src/algorithms/reverse/face.rs
index 9f7a206073..4af2dfd6b0 100644
--- a/crates/fj-kernel/src/algorithms/reverse/face.rs
+++ b/crates/fj-kernel/src/algorithms/reverse/face.rs
@@ -1,4 +1,5 @@
 use crate::{
+    insert::Insert,
     objects::{Face, Objects},
     partial::HasPartial,
     storage::Handle,
@@ -15,10 +16,11 @@ impl Reverse for Handle<Face> {
             .map(|cycle| cycle.clone().reverse(objects))
             .collect::<Result<Vec<_>, _>>()?;
 
-        Face::partial()
+        Ok(Face::partial()
             .with_exterior(exterior)
             .with_interiors(interiors)
             .with_color(self.color())
-            .build(objects)
+            .build(objects)?
+            .insert(objects)?)
     }
 }
diff --git a/crates/fj-kernel/src/algorithms/sweep/edge.rs b/crates/fj-kernel/src/algorithms/sweep/edge.rs
index b4659507a3..e2d98a1754 100644
--- a/crates/fj-kernel/src/algorithms/sweep/edge.rs
+++ b/crates/fj-kernel/src/algorithms/sweep/edge.rs
@@ -3,6 +3,7 @@ use fj_math::{Line, Scalar, Vector};
 
 use crate::{
     algorithms::{reverse::Reverse, transform::TransformObject},
+    insert::Insert,
     objects::{
         Curve, Cycle, Face, GlobalEdge, HalfEdge, Objects, SurfaceVertex,
         Vertex,
@@ -176,10 +177,11 @@ impl Sweep for (Handle<HalfEdge>, Color) {
             objects.cycles.insert(Cycle::new(edges))?
         };
 
-        Face::partial()
+        Ok(Face::partial()
             .with_exterior(cycle)
             .with_color(color)
-            .build(objects)
+            .build(objects)?
+            .insert(objects)?)
     }
 }
 
@@ -191,6 +193,7 @@ mod tests {
     use crate::{
         algorithms::{reverse::Reverse, sweep::Sweep},
         builder::HalfEdgeBuilder,
+        insert::Insert,
         objects::{Cycle, Face, HalfEdge, Objects, SurfaceVertex, Vertex},
         partial::HasPartial,
     };
@@ -204,7 +207,8 @@ mod tests {
                 objects.surfaces.xy_plane(),
                 [[0., 0.], [1., 0.]],
             )
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
 
         let face =
             (half_edge, Color::default()).sweep([0., 0., 1.], &objects)?;
@@ -218,7 +222,8 @@ mod tests {
                         surface.clone(),
                         [[0., 0.], [1., 0.]],
                     )
-                    .build(&objects)?;
+                    .build(&objects)?
+                    .insert(&objects)?;
                 let side_up = HalfEdge::partial()
                     .with_surface(surface.clone())
                     .with_back_vertex(Vertex::partial().with_surface_form(
@@ -228,7 +233,8 @@ mod tests {
                         SurfaceVertex::partial().with_position(Some([1., 1.])),
                     ))
                     .update_as_line_segment()
-                    .build(&objects)?;
+                    .build(&objects)?
+                    .insert(&objects)?;
                 let top = HalfEdge::partial()
                     .with_surface(surface.clone())
                     .with_back_vertex(Vertex::partial().with_surface_form(
@@ -239,6 +245,7 @@ mod tests {
                     ))
                     .update_as_line_segment()
                     .build(&objects)?
+                    .insert(&objects)?
                     .reverse(&objects)?;
                 let side_down =
                     HalfEdge::partial()
@@ -251,13 +258,17 @@ mod tests {
                         ))
                         .update_as_line_segment()
                         .build(&objects)?
+                        .insert(&objects)?
                         .reverse(&objects)?;
 
                 let cycle = objects
                     .cycles
                     .insert(Cycle::new([bottom, side_up, top, side_down]))?;
 
-                Face::partial().with_exterior(cycle).build(&objects)?
+                Face::partial()
+                    .with_exterior(cycle)
+                    .build(&objects)?
+                    .insert(&objects)?
             };
 
         assert_eq!(face, expected_face);
diff --git a/crates/fj-kernel/src/algorithms/sweep/face.rs b/crates/fj-kernel/src/algorithms/sweep/face.rs
index 3919832f7e..cc99370b6d 100644
--- a/crates/fj-kernel/src/algorithms/sweep/face.rs
+++ b/crates/fj-kernel/src/algorithms/sweep/face.rs
@@ -85,6 +85,7 @@ mod tests {
     use crate::{
         algorithms::{reverse::Reverse, transform::TransformObject},
         builder::{FaceBuilder, HalfEdgeBuilder},
+        insert::Insert,
         objects::{Face, HalfEdge, Objects, Sketch},
         partial::HasPartial,
     };
@@ -111,11 +112,13 @@ mod tests {
             .with_surface(surface.clone())
             .with_exterior_polygon_from_points(TRIANGLE)
             .build(&objects)?
+            .insert(&objects)?
             .reverse(&objects)?;
         let top = Face::partial()
             .with_surface(surface.translate(UP, &objects)?)
             .with_exterior_polygon_from_points(TRIANGLE)
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
 
         assert!(solid.find_face(&bottom).is_some());
         assert!(solid.find_face(&top).is_some());
@@ -129,7 +132,8 @@ mod tests {
                         objects.surfaces.xy_plane(),
                         [a, b],
                     )
-                    .build(&objects)?;
+                    .build(&objects)?
+                    .insert(&objects)?;
                 (half_edge, Color::default()).sweep(UP, &objects)
             })
             .collect::<Result<Vec<_>, _>>()?;
@@ -155,11 +159,13 @@ mod tests {
             .with_surface(surface.clone().translate(DOWN, &objects)?)
             .with_exterior_polygon_from_points(TRIANGLE)
             .build(&objects)?
+            .insert(&objects)?
             .reverse(&objects)?;
         let top = Face::partial()
             .with_surface(surface)
             .with_exterior_polygon_from_points(TRIANGLE)
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
 
         assert!(solid.find_face(&bottom).is_some());
         assert!(solid.find_face(&top).is_some());
@@ -174,6 +180,7 @@ mod tests {
                         [a, b],
                     )
                     .build(&objects)?
+                    .insert(&objects)?
                     .reverse(&objects)?;
                 (half_edge, Color::default()).sweep(DOWN, &objects)
             })
diff --git a/crates/fj-kernel/src/algorithms/sweep/vertex.rs b/crates/fj-kernel/src/algorithms/sweep/vertex.rs
index e99c493bc7..0e2d69e4a3 100644
--- a/crates/fj-kernel/src/algorithms/sweep/vertex.rs
+++ b/crates/fj-kernel/src/algorithms/sweep/vertex.rs
@@ -169,6 +169,7 @@ mod tests {
     use crate::{
         algorithms::sweep::Sweep,
         builder::{CurveBuilder, HalfEdgeBuilder},
+        insert::Insert,
         objects::{Curve, HalfEdge, Objects, Vertex},
         partial::HasPartial,
     };
@@ -181,18 +182,21 @@ mod tests {
         let curve = Curve::partial()
             .with_surface(Some(surface.clone()))
             .update_as_u_axis()
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
         let vertex = Vertex::partial()
             .with_position(Some([0.]))
             .with_curve(curve)
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
 
         let half_edge =
             (vertex, surface.clone()).sweep([0., 0., 1.], &objects)?;
 
         let expected_half_edge = HalfEdge::partial()
             .update_as_line_segment_from_points(surface, [[0., 0.], [0., 1.]])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
         assert_eq!(half_edge, expected_half_edge);
         Ok(())
     }
diff --git a/crates/fj-kernel/src/algorithms/transform/face.rs b/crates/fj-kernel/src/algorithms/transform/face.rs
index 833eaebaa7..58c4612a3e 100644
--- a/crates/fj-kernel/src/algorithms/transform/face.rs
+++ b/crates/fj-kernel/src/algorithms/transform/face.rs
@@ -1,6 +1,7 @@
 use fj_math::Transform;
 
 use crate::{
+    insert::Insert,
     objects::{Face, FaceSet, Objects},
     partial::{HasPartial, PartialFace},
     validate::ValidationError,
@@ -26,11 +27,12 @@ impl TransformObject for PartialFace {
         let interiors = self
             .interiors()
             .map(|cycle| -> Result<_, ValidationError> {
-                cycle
+                Ok(cycle
                     .into_partial()
                     .transform(transform, objects)?
                     .with_surface(surface.clone())
-                    .build(objects)
+                    .build(objects)?
+                    .insert(objects)?)
             })
             .collect::<Result<Vec<_>, _>>()?;
 
diff --git a/crates/fj-kernel/src/algorithms/transform/mod.rs b/crates/fj-kernel/src/algorithms/transform/mod.rs
index f262a2750f..5e370e1988 100644
--- a/crates/fj-kernel/src/algorithms/transform/mod.rs
+++ b/crates/fj-kernel/src/algorithms/transform/mod.rs
@@ -13,10 +13,11 @@ mod vertex;
 use fj_math::{Transform, Vector};
 
 use crate::{
+    insert::Insert,
     objects::Objects,
     partial::{HasPartial, MaybePartial, Partial},
     storage::Handle,
-    validate::ValidationError,
+    validate::{Validate, ValidationError},
 };
 
 /// Transform an object
@@ -61,17 +62,20 @@ pub trait TransformObject: Sized {
 
 impl<T> TransformObject for Handle<T>
 where
-    T: HasPartial,
+    T: HasPartial + Insert,
     T::Partial: TransformObject,
+    ValidationError: From<<T as Validate>::Error>,
 {
     fn transform(
         self,
         transform: &Transform,
         objects: &Objects,
     ) -> Result<Self, ValidationError> {
-        self.to_partial()
+        Ok(self
+            .to_partial()
             .transform(transform, objects)?
-            .build(objects)
+            .build(objects)?
+            .insert(objects)?)
     }
 }
 
diff --git a/crates/fj-kernel/src/algorithms/triangulate/mod.rs b/crates/fj-kernel/src/algorithms/triangulate/mod.rs
index 6f9579c70e..a1a0ebe50d 100644
--- a/crates/fj-kernel/src/algorithms/triangulate/mod.rs
+++ b/crates/fj-kernel/src/algorithms/triangulate/mod.rs
@@ -85,6 +85,7 @@ mod tests {
     use crate::{
         algorithms::approx::{Approx, Tolerance},
         builder::FaceBuilder,
+        insert::Insert,
         objects::{Face, Objects},
         partial::HasPartial,
         storage::Handle,
@@ -105,7 +106,8 @@ mod tests {
         let face = Face::partial()
             .with_surface(surface)
             .with_exterior_polygon_from_points([a, b, c, d])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
 
         let a = Point::from(a).to_xyz();
         let b = Point::from(b).to_xyz();
@@ -141,7 +143,8 @@ mod tests {
             .with_surface(surface.clone())
             .with_exterior_polygon_from_points([a, b, c, d])
             .with_interior_polygon_from_points([e, f, g, h])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
 
         let triangles = triangulate(face)?;
 
@@ -201,7 +204,8 @@ mod tests {
         let face = Face::partial()
             .with_surface(surface.clone())
             .with_exterior_polygon_from_points([a, b, c, d, e])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
 
         let triangles = triangulate(face)?;
 
diff --git a/crates/fj-kernel/src/builder/edge.rs b/crates/fj-kernel/src/builder/edge.rs
index c97699b4fa..674183e119 100644
--- a/crates/fj-kernel/src/builder/edge.rs
+++ b/crates/fj-kernel/src/builder/edge.rs
@@ -2,6 +2,7 @@ use fj_interop::ext::ArrayExt;
 use fj_math::{Point, Scalar};
 
 use crate::{
+    insert::Insert,
     objects::{
         Curve, GlobalVertex, Objects, Surface, SurfaceVertex, Vertex,
         VerticesInNormalizedOrder,
@@ -89,7 +90,8 @@ impl HalfEdgeBuilder for PartialHalfEdge {
             .with_position(Some(path.point_from_path_coords(a_curve)))
             .with_surface(curve.surface())
             .with_global_form(Some(global_vertex))
-            .build(objects)?;
+            .build(objects)?
+            .insert(objects)?;
 
         let [back, front] = [a_curve, b_curve].map(|point_curve| {
             Vertex::partial()
diff --git a/crates/fj-kernel/src/builder/shell.rs b/crates/fj-kernel/src/builder/shell.rs
index 867519507b..34534a0227 100644
--- a/crates/fj-kernel/src/builder/shell.rs
+++ b/crates/fj-kernel/src/builder/shell.rs
@@ -6,6 +6,7 @@ use fj_math::Scalar;
 use crate::{
     algorithms::transform::TransformObject,
     builder::{FaceBuilder, HalfEdgeBuilder},
+    insert::Insert,
     objects::{
         Curve, Cycle, Face, FaceSet, HalfEdge, Objects, Shell, Surface,
         SurfaceVertex, Vertex,
@@ -64,6 +65,8 @@ impl<'a> ShellBuilder<'a> {
                 ])
                 .build(self.objects)
                 .unwrap()
+                .insert(self.objects)
+                .unwrap()
         };
 
         let (sides, top_edges) = {
@@ -97,6 +100,8 @@ impl<'a> ShellBuilder<'a> {
                         )
                         .build(self.objects)
                         .unwrap()
+                        .insert(self.objects)
+                        .unwrap()
                 })
                 .collect::<Vec<_>>();
 
@@ -120,6 +125,8 @@ impl<'a> ShellBuilder<'a> {
                         .update_as_line_segment()
                         .build(self.objects)
                         .unwrap()
+                        .insert(self.objects)
+                        .unwrap()
                 })
                 .collect::<Vec<_>>();
 
@@ -157,6 +164,8 @@ impl<'a> ShellBuilder<'a> {
                             .update_as_line_segment()
                             .build(self.objects)
                             .unwrap()
+                            .insert(self.objects)
+                            .unwrap()
                     })
                     .collect::<Vec<_>>()
             };
@@ -180,6 +189,8 @@ impl<'a> ShellBuilder<'a> {
                         .update_as_line_segment()
                         .build(self.objects)
                         .unwrap()
+                        .insert(self.objects)
+                        .unwrap()
                 })
                 .collect::<Vec<_>>();
 
@@ -192,12 +203,16 @@ impl<'a> ShellBuilder<'a> {
                     let cycle = Cycle::partial()
                         .with_half_edges([bottom, side_up, top, side_down])
                         .build(self.objects)
+                        .unwrap()
+                        .insert(self.objects)
                         .unwrap();
 
                     Face::partial()
                         .with_exterior(cycle)
                         .build(self.objects)
                         .unwrap()
+                        .insert(self.objects)
+                        .unwrap()
                 });
 
             (sides, tops)
@@ -232,6 +247,8 @@ impl<'a> ShellBuilder<'a> {
                             ))
                             .build(self.objects)
                             .unwrap()
+                            .insert(self.objects)
+                            .unwrap()
                     });
 
                 [a.clone(), b, c, d, a]
@@ -259,6 +276,8 @@ impl<'a> ShellBuilder<'a> {
                         .with_global_form(edge.global_form().clone())
                         .update_as_line_segment()
                         .build(self.objects)
+                        .unwrap()
+                        .insert(self.objects)
                         .unwrap(),
                 );
             }
@@ -269,6 +288,8 @@ impl<'a> ShellBuilder<'a> {
                 )
                 .build(self.objects)
                 .unwrap()
+                .insert(self.objects)
+                .unwrap()
         };
 
         self.faces.extend([bottom]);
diff --git a/crates/fj-kernel/src/builder/sketch.rs b/crates/fj-kernel/src/builder/sketch.rs
index aad2b9620f..34c66efd2c 100644
--- a/crates/fj-kernel/src/builder/sketch.rs
+++ b/crates/fj-kernel/src/builder/sketch.rs
@@ -1,6 +1,7 @@
 use fj_math::Point;
 
 use crate::{
+    insert::Insert,
     objects::{Face, FaceSet, Objects, Sketch, Surface},
     partial::HasPartial,
     storage::Handle,
@@ -51,6 +52,8 @@ impl<'a> SketchBuilder<'a> {
             .with_surface(surface.clone())
             .with_exterior_polygon_from_points(points)
             .build(self.objects)
+            .unwrap()
+            .insert(self.objects)
             .unwrap()]);
         self
     }
diff --git a/crates/fj-kernel/src/iter.rs b/crates/fj-kernel/src/iter.rs
index 2b73c8bd3b..61d91aa1d7 100644
--- a/crates/fj-kernel/src/iter.rs
+++ b/crates/fj-kernel/src/iter.rs
@@ -361,6 +361,7 @@ impl<T> Iterator for Iter<T> {
 mod tests {
     use crate::{
         builder::{CurveBuilder, CycleBuilder, FaceBuilder, HalfEdgeBuilder},
+        insert::Insert,
         objects::{
             Curve, Cycle, Face, GlobalCurve, GlobalVertex, HalfEdge, Objects,
             Shell, Sketch, Solid, SurfaceVertex, Vertex,
@@ -378,7 +379,8 @@ mod tests {
         let object = Curve::partial()
             .with_surface(Some(surface))
             .update_as_u_axis()
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
 
         assert_eq!(1, object.curve_iter().count());
         assert_eq!(0, object.cycle_iter().count());
@@ -406,7 +408,8 @@ mod tests {
                 [[0., 0.], [1., 0.], [0., 1.]],
             )
             .close_with_line_segment()
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects);
 
         assert_eq!(3, object.curve_iter().count());
         assert_eq!(1, object.cycle_iter().count());
@@ -431,7 +434,8 @@ mod tests {
         let object = Face::partial()
             .with_surface(surface)
             .with_exterior_polygon_from_points([[0., 0.], [1., 0.], [0., 1.]])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
 
         assert_eq!(3, object.curve_iter().count());
         assert_eq!(1, object.cycle_iter().count());
@@ -501,7 +505,8 @@ mod tests {
                 objects.surfaces.xy_plane(),
                 [[0., 0.], [1., 0.]],
             )
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
 
         assert_eq!(1, object.curve_iter().count());
         assert_eq!(0, object.cycle_iter().count());
@@ -547,7 +552,8 @@ mod tests {
         let face = Face::partial()
             .with_surface(surface)
             .with_exterior_polygon_from_points([[0., 0.], [1., 0.], [0., 1.]])
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
         let object = Sketch::builder(&objects).with_faces([face]).build();
 
         assert_eq!(3, object.curve_iter().count());
@@ -613,7 +619,8 @@ mod tests {
         let curve = Curve::partial()
             .with_surface(Some(surface.clone()))
             .update_as_u_axis()
-            .build(&objects)?;
+            .build(&objects)?
+            .insert(&objects)?;
         let global_vertex = objects
             .global_vertices
             .insert(GlobalVertex::from_position([0., 0., 0.]))?;
diff --git a/crates/fj-kernel/src/partial/maybe_partial.rs b/crates/fj-kernel/src/partial/maybe_partial.rs
index ecc6ad9eec..4a232fb714 100644
--- a/crates/fj-kernel/src/partial/maybe_partial.rs
+++ b/crates/fj-kernel/src/partial/maybe_partial.rs
@@ -1,13 +1,14 @@
 use fj_math::Point;
 
 use crate::{
+    insert::Insert,
     objects::{
         Curve, GlobalCurve, GlobalEdge, GlobalVertex, HalfEdge, Objects,
         Surface, SurfaceVertex, Vertex,
     },
     path::SurfacePath,
     storage::Handle,
-    validate::ValidationError,
+    validate::{Validate, ValidationError},
 };
 
 use super::{HasPartial, Partial};
@@ -91,9 +92,15 @@ impl<T: HasPartial> MaybePartial<T> {
     pub fn into_full(
         self,
         objects: &Objects,
-    ) -> Result<Handle<T>, ValidationError> {
+    ) -> Result<Handle<T>, ValidationError>
+    where
+        T: Insert,
+        ValidationError: From<<T as Validate>::Error>,
+    {
         match self {
-            Self::Partial(partial) => partial.build(objects),
+            Self::Partial(partial) => {
+                Ok(partial.build(objects)?.insert(objects)?)
+            }
             Self::Full(full) => Ok(full),
         }
     }
diff --git a/crates/fj-kernel/src/partial/objects/curve.rs b/crates/fj-kernel/src/partial/objects/curve.rs
index f8840e1a01..6c08f77fd3 100644
--- a/crates/fj-kernel/src/partial/objects/curve.rs
+++ b/crates/fj-kernel/src/partial/objects/curve.rs
@@ -80,10 +80,7 @@ impl PartialCurve {
     }
 
     /// Build a full [`Curve`] from the partial curve
-    pub fn build(
-        self,
-        objects: &Objects,
-    ) -> Result<Handle<Curve>, ValidationError> {
+    pub fn build(self, objects: &Objects) -> Result<Curve, ValidationError> {
         let path = self.path.expect("Can't build `Curve` without path");
         let surface =
             self.surface.expect("Can't build `Curve` without surface");
@@ -94,9 +91,7 @@ impl PartialCurve {
         }
         .into_full(objects)?;
 
-        Ok(objects
-            .curves
-            .insert(Curve::new(surface, path, global_form))?)
+        Ok(Curve::new(surface, path, global_form))
     }
 }
 
@@ -128,12 +123,8 @@ impl PartialGlobalCurve {
     }
 
     /// Build a full [`GlobalCurve`] from the partial global curve
-    pub fn build(
-        self,
-        objects: &Objects,
-    ) -> Result<Handle<GlobalCurve>, ValidationError> {
-        let global_curve = objects.global_curves.insert(GlobalCurve)?;
-        Ok(global_curve)
+    pub fn build(self, _: &Objects) -> Result<GlobalCurve, ValidationError> {
+        Ok(GlobalCurve)
     }
 }
 
diff --git a/crates/fj-kernel/src/partial/objects/cycle.rs b/crates/fj-kernel/src/partial/objects/cycle.rs
index d27531b531..bbefef9672 100644
--- a/crates/fj-kernel/src/partial/objects/cycle.rs
+++ b/crates/fj-kernel/src/partial/objects/cycle.rs
@@ -86,7 +86,7 @@ impl PartialCycle {
     pub fn build(
         mut self,
         objects: &Objects,
-    ) -> Result<Handle<Cycle>, ValidationError> {
+    ) -> Result<Cycle, ValidationError> {
         // Check that the cycle is closed. This will lead to a panic further
         // down anyway, but that panic would be super-confusing. This one should
         // be a bit more explicit on what is wrong.
@@ -142,7 +142,7 @@ impl PartialCycle {
             half_edges.push(half_edge);
         }
 
-        Ok(objects.cycles.insert(Cycle::new(half_edges))?)
+        Ok(Cycle::new(half_edges))
     }
 }
 
diff --git a/crates/fj-kernel/src/partial/objects/edge.rs b/crates/fj-kernel/src/partial/objects/edge.rs
index fb8d268ad0..f2d7e3cea7 100644
--- a/crates/fj-kernel/src/partial/objects/edge.rs
+++ b/crates/fj-kernel/src/partial/objects/edge.rs
@@ -102,10 +102,7 @@ impl PartialHalfEdge {
     }
 
     /// Build a full [`HalfEdge`] from the partial half-edge
-    pub fn build(
-        self,
-        objects: &Objects,
-    ) -> Result<Handle<HalfEdge>, ValidationError> {
+    pub fn build(self, objects: &Objects) -> Result<HalfEdge, ValidationError> {
         let curve = self.curve.into_full(objects)?;
         let vertices = self.vertices.try_map_ext(|vertex| {
             vertex
@@ -120,9 +117,7 @@ impl PartialHalfEdge {
             })
             .into_full(objects)?;
 
-        Ok(objects
-            .half_edges
-            .insert(HalfEdge::new(vertices, global_form))?)
+        Ok(HalfEdge::new(vertices, global_form))
     }
 }
 
@@ -202,16 +197,14 @@ impl PartialGlobalEdge {
     pub fn build(
         self,
         objects: &Objects,
-    ) -> Result<Handle<GlobalEdge>, ValidationError> {
+    ) -> Result<GlobalEdge, ValidationError> {
         let curve = self.curve.into_full(objects)?;
         let vertices = self
             .vertices
             .expect("Can't build `GlobalEdge` without vertices")
             .try_map_ext(|global_vertex| global_vertex.into_full(objects))?;
 
-        Ok(objects
-            .global_edges
-            .insert(GlobalEdge::new(curve, vertices))?)
+        Ok(GlobalEdge::new(curve, vertices))
     }
 }
 
diff --git a/crates/fj-kernel/src/partial/objects/face.rs b/crates/fj-kernel/src/partial/objects/face.rs
index c2dbf2a333..f2dcc8460b 100644
--- a/crates/fj-kernel/src/partial/objects/face.rs
+++ b/crates/fj-kernel/src/partial/objects/face.rs
@@ -84,10 +84,7 @@ impl PartialFace {
     }
 
     /// Construct a polygon from a list of points
-    pub fn build(
-        self,
-        objects: &Objects,
-    ) -> Result<Handle<Face>, ValidationError> {
+    pub fn build(self, objects: &Objects) -> Result<Face, ValidationError> {
         let exterior = self.exterior.into_full(objects)?;
         let interiors = self
             .interiors
@@ -96,9 +93,7 @@ impl PartialFace {
             .collect::<Result<Vec<_>, _>>()?;
         let color = self.color.unwrap_or_default();
 
-        Ok(objects
-            .faces
-            .insert(Face::new(exterior, interiors, color))?)
+        Ok(Face::new(exterior, interiors, color))
     }
 }
 
diff --git a/crates/fj-kernel/src/partial/objects/mod.rs b/crates/fj-kernel/src/partial/objects/mod.rs
index 5ab9c57b7b..277752a94b 100644
--- a/crates/fj-kernel/src/partial/objects/mod.rs
+++ b/crates/fj-kernel/src/partial/objects/mod.rs
@@ -4,12 +4,9 @@ pub mod edge;
 pub mod face;
 pub mod vertex;
 
-use crate::{
-    objects::{
-        Curve, Cycle, Face, GlobalCurve, GlobalEdge, GlobalVertex, HalfEdge,
-        Objects, SurfaceVertex, Vertex,
-    },
-    storage::Handle,
+use crate::objects::{
+    Curve, Cycle, Face, GlobalCurve, GlobalEdge, GlobalVertex, HalfEdge,
+    Objects, SurfaceVertex, Vertex,
 };
 
 use super::{
@@ -34,7 +31,7 @@ macro_rules! impl_traits {
 
                 fn build(self, objects: &Objects)
                     -> Result<
-                        Handle<Self::Full>,
+                        Self::Full,
                         crate::validate::ValidationError
                     >
                 {
diff --git a/crates/fj-kernel/src/partial/objects/vertex.rs b/crates/fj-kernel/src/partial/objects/vertex.rs
index f3cd84539a..e7693ca502 100644
--- a/crates/fj-kernel/src/partial/objects/vertex.rs
+++ b/crates/fj-kernel/src/partial/objects/vertex.rs
@@ -76,10 +76,7 @@ impl PartialVertex {
     /// Panics, if position has not been provided.
     ///
     /// Panics, if curve has not been provided.
-    pub fn build(
-        self,
-        objects: &Objects,
-    ) -> Result<Handle<Vertex>, ValidationError> {
+    pub fn build(self, objects: &Objects) -> Result<Vertex, ValidationError> {
         let position = self
             .position
             .expect("Cant' build `Vertex` without position");
@@ -98,11 +95,7 @@ impl PartialVertex {
             })
             .into_full(objects)?;
 
-        Ok(objects.vertices.insert(Vertex::new(
-            position,
-            curve,
-            surface_form,
-        ))?)
+        Ok(Vertex::new(position, curve, surface_form))
     }
 }
 
@@ -185,7 +178,7 @@ impl PartialSurfaceVertex {
     pub fn build(
         self,
         objects: &Objects,
-    ) -> Result<Handle<SurfaceVertex>, ValidationError> {
+    ) -> Result<SurfaceVertex, ValidationError> {
         let position = self
             .position
             .expect("Can't build `SurfaceVertex` without position");
@@ -200,11 +193,7 @@ impl PartialSurfaceVertex {
             })
             .into_full(objects)?;
 
-        Ok(objects.surface_vertices.insert(SurfaceVertex::new(
-            position,
-            surface,
-            global_form,
-        ))?)
+        Ok(SurfaceVertex::new(position, surface, global_form))
     }
 }
 
@@ -251,17 +240,12 @@ impl PartialGlobalVertex {
     }
 
     /// Build a full [`GlobalVertex`] from the partial global vertex
-    pub fn build(
-        self,
-        objects: &Objects,
-    ) -> Result<Handle<GlobalVertex>, ValidationError> {
+    pub fn build(self, _: &Objects) -> Result<GlobalVertex, ValidationError> {
         let position = self
             .position
             .expect("Can't build a `GlobalVertex` without a position");
 
-        Ok(objects
-            .global_vertices
-            .insert(GlobalVertex::from_position(position))?)
+        Ok(GlobalVertex::from_position(position))
     }
 }
 
diff --git a/crates/fj-kernel/src/partial/traits.rs b/crates/fj-kernel/src/partial/traits.rs
index e18bf1c4a4..c0b1a1d54a 100644
--- a/crates/fj-kernel/src/partial/traits.rs
+++ b/crates/fj-kernel/src/partial/traits.rs
@@ -1,4 +1,4 @@
-use crate::{objects::Objects, storage::Handle, validate::ValidationError};
+use crate::{objects::Objects, validate::ValidationError};
 
 /// Implemented for objects that a partial object type exists for
 ///
@@ -80,8 +80,5 @@ pub trait Partial: Default + for<'a> From<&'a Self::Full> {
     /// Calling `build` on a partial object that can't infer its missing parts
     /// is considered a programmer error, hence why this method doesn't return a
     /// [`Result`].
-    fn build(
-        self,
-        objects: &Objects,
-    ) -> Result<Handle<Self::Full>, ValidationError>;
+    fn build(self, objects: &Objects) -> Result<Self::Full, ValidationError>;
 }
diff --git a/crates/fj-kernel/src/validate/cycle.rs b/crates/fj-kernel/src/validate/cycle.rs
index d20c74750e..45824c3013 100644
--- a/crates/fj-kernel/src/validate/cycle.rs
+++ b/crates/fj-kernel/src/validate/cycle.rs
@@ -67,9 +67,10 @@ impl CycleValidationError {
 mod tests {
     use crate::{
         builder::{CycleBuilder, HalfEdgeBuilder, VertexBuilder},
+        insert::Insert,
         objects::{Cycle, Objects},
         partial::HasPartial,
-        validate::Validate,
+        validate::{Validate, ValidationError},
     };
 
     #[test]
@@ -102,7 +103,9 @@ mod tests {
 
             let half_edges = half_edges
                 .into_iter()
-                .map(|half_edge| half_edge.build(&objects))
+                .map(|half_edge| -> anyhow::Result<_, ValidationError> {
+                    Ok(half_edge.build(&objects)?.insert(&objects)?)
+                })
                 .collect::<Result<Vec<_>, _>>()?;
 
             Cycle::new(half_edges)
diff --git a/crates/fj-kernel/src/validate/edge.rs b/crates/fj-kernel/src/validate/edge.rs
index ab105ea324..7a4b837d1f 100644
--- a/crates/fj-kernel/src/validate/edge.rs
+++ b/crates/fj-kernel/src/validate/edge.rs
@@ -202,9 +202,10 @@ mod tests {
 
     use crate::{
         builder::{HalfEdgeBuilder, VertexBuilder},
+        insert::Insert,
         objects::{GlobalCurve, HalfEdge, Objects},
         partial::HasPartial,
-        validate::Validate,
+        validate::{Validate, ValidationError},
     };
 
     #[test]
@@ -223,7 +224,8 @@ mod tests {
                 .to_partial()
                 // Arranging for an equal but not identical curve here.
                 .with_curve(valid.curve().to_partial())
-                .build(&objects)?;
+                .build(&objects)?
+                .insert(&objects)?;
 
             HalfEdge::new(vertices, valid.global_form().clone())
         };
@@ -250,7 +252,8 @@ mod tests {
                 .global_form()
                 .to_partial()
                 .with_curve(Some(objects.global_curves.insert(GlobalCurve)?))
-                .build(&objects)?,
+                .build(&objects)?
+                .insert(&objects)?,
         );
 
         assert!(valid.validate().is_ok());
@@ -282,7 +285,8 @@ mod tests {
                         // Creating equal but not identical vertices here.
                         .map(|vertex| vertex.to_partial()),
                 ))
-                .build(&objects)?,
+                .build(&objects)?
+                .insert(&objects)?,
         );
 
         assert!(valid.validate().is_ok());
@@ -302,13 +306,16 @@ mod tests {
             )
             .build(&objects)?;
         let invalid = HalfEdge::new(
-            valid.vertices().clone().try_map_ext(|vertex| {
-                vertex
-                    .to_partial()
-                    .with_position(Some([0.]))
-                    .infer_surface_form()
-                    .build(&objects)
-            })?,
+            valid.vertices().clone().try_map_ext(
+                |vertex| -> anyhow::Result<_, ValidationError> {
+                    Ok(vertex
+                        .to_partial()
+                        .with_position(Some([0.]))
+                        .infer_surface_form()
+                        .build(&objects)?
+                        .insert(&objects)?)
+                },
+            )?,
             valid.global_form().clone(),
         );
 
diff --git a/crates/fj-kernel/src/validate/face.rs b/crates/fj-kernel/src/validate/face.rs
index 098b5ea28a..6ef0345a28 100644
--- a/crates/fj-kernel/src/validate/face.rs
+++ b/crates/fj-kernel/src/validate/face.rs
@@ -106,6 +106,7 @@ mod tests {
     use crate::{
         algorithms::reverse::Reverse,
         builder::{CycleBuilder, FaceBuilder},
+        insert::Insert,
         objects::{Cycle, Face, Objects},
         partial::HasPartial,
         validate::Validate,
@@ -127,7 +128,8 @@ mod tests {
                     [[1., 1.], [1., 2.], [2., 1.]],
                 )
                 .close_with_line_segment()
-                .build(&objects)?];
+                .build(&objects)?
+                .insert(&objects)?];
 
             Face::new(valid.exterior().clone(), interiors, valid.color())
         };
diff --git a/crates/fj-kernel/src/validate/vertex.rs b/crates/fj-kernel/src/validate/vertex.rs
index 39d6d082dd..0ef103fe98 100644
--- a/crates/fj-kernel/src/validate/vertex.rs
+++ b/crates/fj-kernel/src/validate/vertex.rs
@@ -180,6 +180,7 @@ impl SurfaceVertexValidationError {
 mod tests {
     use crate::{
         builder::{CurveBuilder, SurfaceVertexBuilder},
+        insert::Insert,
         objects::{Curve, GlobalVertex, Objects, SurfaceVertex, Vertex},
         partial::HasPartial,
         validate::Validate,
@@ -204,7 +205,8 @@ mod tests {
                 .surface_form()
                 .to_partial()
                 .with_surface(Some(objects.surfaces.xz_plane()))
-                .build(&objects)?,
+                .build(&objects)?
+                .insert(&objects)?,
         );
 
         assert!(valid.validate().is_ok());
@@ -233,7 +235,8 @@ mod tests {
                 .to_partial()
                 .with_position(Some([1., 0.]))
                 .infer_global_form()
-                .build(&objects)?,
+                .build(&objects)?
+                .insert(&objects)?,
         );
 
         assert!(valid.validate().is_ok());
diff --git a/crates/fj-operations/src/difference_2d.rs b/crates/fj-operations/src/difference_2d.rs
index 341ac2b305..54b60414a3 100644
--- a/crates/fj-operations/src/difference_2d.rs
+++ b/crates/fj-operations/src/difference_2d.rs
@@ -3,6 +3,7 @@ use std::ops::Deref;
 use fj_interop::{debug::DebugInfo, ext::ArrayExt, mesh::Color};
 use fj_kernel::{
     algorithms::reverse::Reverse,
+    insert::Insert,
     iter::ObjectIters,
     objects::{Face, Objects, Sketch},
     partial::HasPartial,
@@ -83,7 +84,8 @@ impl Shape for fj::Difference2d {
                     .with_exterior(exterior)
                     .with_interiors(interiors)
                     .with_color(Color(self.color()))
-                    .build(objects)?,
+                    .build(objects)?
+                    .insert(objects)?,
             );
         }
 
diff --git a/crates/fj-operations/src/sketch.rs b/crates/fj-operations/src/sketch.rs
index 83ab1911c4..90e596d2ff 100644
--- a/crates/fj-operations/src/sketch.rs
+++ b/crates/fj-operations/src/sketch.rs
@@ -3,6 +3,7 @@ use std::ops::Deref;
 use fj_interop::{debug::DebugInfo, mesh::Color};
 use fj_kernel::{
     builder::{FaceBuilder, HalfEdgeBuilder},
+    insert::Insert,
     objects::{Cycle, Face, HalfEdge, Objects, Sketch},
     partial::HasPartial,
     validate::ValidationError,
@@ -29,13 +30,15 @@ impl Shape for fj::Sketch {
                 let half_edge = HalfEdge::partial()
                     .with_surface(surface)
                     .update_as_circle_from_radius(circle.radius(), objects)?
-                    .build(objects)?;
+                    .build(objects)?
+                    .insert(objects)?;
                 let cycle = objects.cycles.insert(Cycle::new([half_edge]))?;
 
                 Face::partial()
                     .with_exterior(cycle)
                     .with_color(Color(self.color()))
                     .build(objects)?
+                    .insert(objects)?
             }
             fj::Chain::PolyChain(poly_chain) => {
                 let points =
@@ -46,6 +49,7 @@ impl Shape for fj::Sketch {
                     .with_exterior_polygon_from_points(points)
                     .with_color(Color(self.color()))
                     .build(objects)?
+                    .insert(objects)?
             }
         };