diff --git a/crates/fj-kernel/src/algorithms/approx/curve.rs b/crates/fj-kernel/src/algorithms/approx/curve.rs
index 16f9e26e4..45b893d20 100644
--- a/crates/fj-kernel/src/algorithms/approx/curve.rs
+++ b/crates/fj-kernel/src/algorithms/approx/curve.rs
@@ -199,8 +199,8 @@ mod tests {
         algorithms::approx::{path::RangeOnPath, Approx, ApproxPoint},
         builder::CurveBuilder,
         insert::Insert,
-        objects::{Curve, Objects, Surface},
-        partial::HasPartial,
+        objects::{Objects, Surface},
+        partial::PartialCurve,
         path::GlobalPath,
     };
 
@@ -213,11 +213,13 @@ mod tests {
         let surface = objects
             .surfaces
             .insert(Surface::new(GlobalPath::x_axis(), [0., 0., 1.]))?;
-        let curve = Curve::partial()
-            .with_surface(Some(surface))
-            .update_as_line_from_points([[1., 1.], [2., 1.]])
-            .build(&objects)?
-            .insert(&objects)?;
+        let curve = PartialCurve {
+            surface: Some(surface),
+            ..Default::default()
+        }
+        .update_as_line_from_points([[1., 1.], [2., 1.]])
+        .build(&objects)?
+        .insert(&objects)?;
         let range = RangeOnPath::from([[0.], [1.]]);
 
         let approx = (&curve, range).approx(1.);
@@ -235,11 +237,13 @@ mod tests {
             GlobalPath::circle_from_radius(1.),
             [0., 0., 1.],
         ))?;
-        let curve = Curve::partial()
-            .with_surface(Some(surface))
-            .update_as_line_from_points([[1., 1.], [1., 2.]])
-            .build(&objects)?
-            .insert(&objects)?;
+        let curve = PartialCurve {
+            surface: Some(surface),
+            ..Default::default()
+        }
+        .update_as_line_from_points([[1., 1.], [1., 2.]])
+        .build(&objects)?
+        .insert(&objects)?;
         let range = RangeOnPath::from([[0.], [1.]]);
 
         let approx = (&curve, range).approx(1.);
@@ -255,11 +259,13 @@ mod tests {
         let path = GlobalPath::circle_from_radius(1.);
         let surface =
             objects.surfaces.insert(Surface::new(path, [0., 0., 1.]))?;
-        let curve = Curve::partial()
-            .with_surface(Some(surface.clone()))
-            .update_as_line_from_points([[0., 1.], [1., 1.]])
-            .build(&objects)?
-            .insert(&objects)?;
+        let curve = PartialCurve {
+            surface: Some(surface.clone()),
+            ..Default::default()
+        }
+        .update_as_line_from_points([[0., 1.], [1., 1.]])
+        .build(&objects)?
+        .insert(&objects)?;
 
         let range = RangeOnPath::from([[0.], [TAU]]);
         let tolerance = 1.;
@@ -288,11 +294,13 @@ mod tests {
         let surface = objects
             .surfaces
             .insert(Surface::new(GlobalPath::x_axis(), [0., 0., 1.]))?;
-        let curve = Curve::partial()
-            .with_surface(Some(surface))
-            .update_as_circle_from_radius(1.)
-            .build(&objects)?
-            .insert(&objects)?;
+        let curve = PartialCurve {
+            surface: Some(surface),
+            ..Default::default()
+        }
+        .update_as_circle_from_radius(1.)
+        .build(&objects)?
+        .insert(&objects)?;
 
         let range = RangeOnPath::from([[0.], [TAU]]);
         let tolerance = 1.;
diff --git a/crates/fj-kernel/src/algorithms/intersect/curve_edge.rs b/crates/fj-kernel/src/algorithms/intersect/curve_edge.rs
index 4b6376820..1b6d14a8b 100644
--- a/crates/fj-kernel/src/algorithms/intersect/curve_edge.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/curve_edge.rs
@@ -76,8 +76,8 @@ mod tests {
 
     use crate::{
         builder::{CurveBuilder, HalfEdgeBuilder},
-        objects::{Curve, HalfEdge, Objects},
-        partial::HasPartial,
+        objects::{HalfEdge, Objects},
+        partial::{HasPartial, PartialCurve},
     };
 
     use super::CurveEdgeIntersection;
@@ -87,10 +87,12 @@ mod tests {
         let objects = Objects::new();
 
         let surface = objects.surfaces.xy_plane();
-        let curve = Curve::partial()
-            .with_surface(Some(surface.clone()))
-            .update_as_u_axis()
-            .build(&objects)?;
+        let curve = PartialCurve {
+            surface: Some(surface.clone()),
+            ..Default::default()
+        }
+        .update_as_u_axis()
+        .build(&objects)?;
         let half_edge = HalfEdge::partial()
             .update_as_line_segment_from_points(surface, [[1., -1.], [1., 1.]])
             .build(&objects)?;
@@ -111,10 +113,12 @@ mod tests {
         let objects = Objects::new();
 
         let surface = objects.surfaces.xy_plane();
-        let curve = Curve::partial()
-            .with_surface(Some(surface.clone()))
-            .update_as_u_axis()
-            .build(&objects)?;
+        let curve = PartialCurve {
+            surface: Some(surface.clone()),
+            ..Default::default()
+        }
+        .update_as_u_axis()
+        .build(&objects)?;
         let half_edge = HalfEdge::partial()
             .update_as_line_segment_from_points(
                 surface,
@@ -138,10 +142,12 @@ mod tests {
         let objects = Objects::new();
 
         let surface = objects.surfaces.xy_plane();
-        let curve = Curve::partial()
-            .with_surface(Some(surface.clone()))
-            .update_as_u_axis()
-            .build(&objects)?;
+        let curve = PartialCurve {
+            surface: Some(surface.clone()),
+            ..Default::default()
+        }
+        .update_as_u_axis()
+        .build(&objects)?;
         let half_edge = HalfEdge::partial()
             .update_as_line_segment_from_points(
                 surface,
@@ -160,10 +166,12 @@ mod tests {
         let objects = Objects::new();
 
         let surface = objects.surfaces.xy_plane();
-        let curve = Curve::partial()
-            .with_surface(Some(surface.clone()))
-            .update_as_u_axis()
-            .build(&objects)?;
+        let curve = PartialCurve {
+            surface: Some(surface.clone()),
+            ..Default::default()
+        }
+        .update_as_u_axis()
+        .build(&objects)?;
         let half_edge = HalfEdge::partial()
             .update_as_line_segment_from_points(surface, [[-1., 0.], [1., 0.]])
             .build(&objects)?;
diff --git a/crates/fj-kernel/src/algorithms/intersect/curve_face.rs b/crates/fj-kernel/src/algorithms/intersect/curve_face.rs
index 9e87ec130..c87c06d12 100644
--- a/crates/fj-kernel/src/algorithms/intersect/curve_face.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/curve_face.rs
@@ -151,8 +151,8 @@ where
 mod tests {
     use crate::{
         builder::{CurveBuilder, FaceBuilder},
-        objects::{Curve, Face, Objects},
-        partial::HasPartial,
+        objects::{Face, Objects},
+        partial::{HasPartial, PartialCurve},
     };
 
     use super::CurveFaceIntersection;
@@ -163,10 +163,12 @@ mod tests {
 
         let surface = objects.surfaces.xy_plane();
 
-        let curve = Curve::partial()
-            .with_surface(Some(surface.clone()))
-            .update_as_line_from_points([[-3., 0.], [-2., 0.]])
-            .build(&objects)?;
+        let curve = PartialCurve {
+            surface: Some(surface.clone()),
+            ..Default::default()
+        }
+        .update_as_line_from_points([[-3., 0.], [-2., 0.]])
+        .build(&objects)?;
 
         #[rustfmt::skip]
         let exterior = [
diff --git a/crates/fj-kernel/src/algorithms/intersect/face_face.rs b/crates/fj-kernel/src/algorithms/intersect/face_face.rs
index 6c3fb9c77..d197b5b81 100644
--- a/crates/fj-kernel/src/algorithms/intersect/face_face.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/face_face.rs
@@ -72,8 +72,8 @@ mod tests {
         algorithms::intersect::CurveFaceIntersection,
         builder::{CurveBuilder, FaceBuilder},
         insert::Insert,
-        objects::{Curve, Face, Objects},
-        partial::HasPartial,
+        objects::{Face, Objects},
+        partial::{HasPartial, PartialCurve},
         validate::ValidationError,
     };
 
@@ -129,11 +129,13 @@ mod tests {
 
         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)?)
+                Ok(PartialCurve {
+                    surface: Some(surface),
+                    ..Default::default()
+                }
+                .update_as_line_from_points([[0., 0.], [1., 0.]])
+                .build(&objects)?
+                .insert(&objects)?)
             })?;
         let expected_intervals =
             CurveFaceIntersection::from_intervals([[[-1.], [1.]]]);
diff --git a/crates/fj-kernel/src/algorithms/intersect/surface_surface.rs b/crates/fj-kernel/src/algorithms/intersect/surface_surface.rs
index 7481608f9..ebc7c2d16 100644
--- a/crates/fj-kernel/src/algorithms/intersect/surface_surface.rs
+++ b/crates/fj-kernel/src/algorithms/intersect/surface_surface.rs
@@ -91,11 +91,8 @@ mod tests {
     use pretty_assertions::assert_eq;
 
     use crate::{
-        algorithms::transform::TransformObject,
-        builder::CurveBuilder,
-        insert::Insert,
-        objects::{Curve, Objects},
-        partial::HasPartial,
+        algorithms::transform::TransformObject, builder::CurveBuilder,
+        insert::Insert, objects::Objects, partial::PartialCurve,
     };
 
     use super::SurfaceSurfaceIntersection;
@@ -122,16 +119,20 @@ mod tests {
             None,
         );
 
-        let expected_xy = Curve::partial()
-            .with_surface(Some(xy.clone()))
-            .update_as_u_axis()
-            .build(&objects)?
-            .insert(&objects)?;
-        let expected_xz = Curve::partial()
-            .with_surface(Some(xz.clone()))
-            .update_as_u_axis()
-            .build(&objects)?
-            .insert(&objects)?;
+        let expected_xy = PartialCurve {
+            surface: Some(xy.clone()),
+            ..Default::default()
+        }
+        .update_as_u_axis()
+        .build(&objects)?
+        .insert(&objects)?;
+        let expected_xz = PartialCurve {
+            surface: Some(xz.clone()),
+            ..Default::default()
+        }
+        .update_as_u_axis()
+        .build(&objects)?
+        .insert(&objects)?;
 
         assert_eq!(
             SurfaceSurfaceIntersection::compute([xy, xz], &objects)?,
diff --git a/crates/fj-kernel/src/algorithms/sweep/vertex.rs b/crates/fj-kernel/src/algorithms/sweep/vertex.rs
index 0e2d69e4a..750a0c338 100644
--- a/crates/fj-kernel/src/algorithms/sweep/vertex.rs
+++ b/crates/fj-kernel/src/algorithms/sweep/vertex.rs
@@ -170,8 +170,8 @@ mod tests {
         algorithms::sweep::Sweep,
         builder::{CurveBuilder, HalfEdgeBuilder},
         insert::Insert,
-        objects::{Curve, HalfEdge, Objects, Vertex},
-        partial::HasPartial,
+        objects::{HalfEdge, Objects, Vertex},
+        partial::{HasPartial, PartialCurve},
     };
 
     #[test]
@@ -179,11 +179,13 @@ mod tests {
         let objects = Objects::new();
 
         let surface = objects.surfaces.xz_plane();
-        let curve = Curve::partial()
-            .with_surface(Some(surface.clone()))
-            .update_as_u_axis()
-            .build(&objects)?
-            .insert(&objects)?;
+        let curve = PartialCurve {
+            surface: Some(surface.clone()),
+            ..Default::default()
+        }
+        .update_as_u_axis()
+        .build(&objects)?
+        .insert(&objects)?;
         let vertex = Vertex::partial()
             .with_position(Some([0.]))
             .with_curve(curve)
diff --git a/crates/fj-kernel/src/algorithms/transform/curve.rs b/crates/fj-kernel/src/algorithms/transform/curve.rs
index ce81ca8d9..351f1e689 100644
--- a/crates/fj-kernel/src/algorithms/transform/curve.rs
+++ b/crates/fj-kernel/src/algorithms/transform/curve.rs
@@ -41,9 +41,9 @@ impl TransformObject for PartialCurve {
         // coordinates, and thus transforming `surface` takes care of it.
         Ok(PartialCurve {
             path: self.path,
+            surface,
             ..Default::default()
         }
-        .with_surface(surface)
         .with_global_form(global_form))
     }
 }
diff --git a/crates/fj-kernel/src/builder/cycle.rs b/crates/fj-kernel/src/builder/cycle.rs
index 09f25cd30..a2499bbd2 100644
--- a/crates/fj-kernel/src/builder/cycle.rs
+++ b/crates/fj-kernel/src/builder/cycle.rs
@@ -1,8 +1,8 @@
 use fj_math::Point;
 
 use crate::{
-    objects::{Curve, HalfEdge, Surface, SurfaceVertex, Vertex},
-    partial::{HasPartial, MaybePartial, PartialCycle},
+    objects::{HalfEdge, Surface, SurfaceVertex, Vertex},
+    partial::{HasPartial, MaybePartial, PartialCurve, PartialCycle},
     storage::Handle,
 };
 
@@ -64,9 +64,11 @@ impl CycleBuilder for PartialCycle {
 
                 previous = Some(vertex_next.clone());
 
-                let curve = Curve::partial()
-                    .with_surface(Some(surface.clone()))
-                    .update_as_line_from_points([position_prev, position_next]);
+                let curve = PartialCurve {
+                    surface: Some(surface.clone()),
+                    ..Default::default()
+                }
+                .update_as_line_from_points([position_prev, position_next]);
 
                 let vertices = [(0., vertex_prev), (1., vertex_next)].map(
                     |(position, surface_form)| {
diff --git a/crates/fj-kernel/src/builder/edge.rs b/crates/fj-kernel/src/builder/edge.rs
index 9a7eab91e..a1cf231f6 100644
--- a/crates/fj-kernel/src/builder/edge.rs
+++ b/crates/fj-kernel/src/builder/edge.rs
@@ -7,7 +7,10 @@ use crate::{
         Curve, GlobalVertex, Objects, Surface, SurfaceVertex, Vertex,
         VerticesInNormalizedOrder,
     },
-    partial::{HasPartial, MaybePartial, PartialGlobalEdge, PartialHalfEdge},
+    partial::{
+        HasPartial, MaybePartial, PartialCurve, PartialGlobalEdge,
+        PartialHalfEdge,
+    },
     storage::Handle,
     validate::ValidationError,
 };
@@ -138,10 +141,12 @@ impl HalfEdgeBuilder for PartialHalfEdge {
                 .expect("Can't infer line segment without surface position")
         });
 
-        let curve = Curve::partial()
-            .with_global_form(Some(self.extract_global_curve()))
-            .with_surface(Some(surface))
-            .update_as_line_from_points(points);
+        let curve = PartialCurve {
+            surface: Some(surface),
+            ..Default::default()
+        }
+        .with_global_form(Some(self.extract_global_curve()))
+        .update_as_line_from_points(points);
 
         let [back, front] = {
             let vertices = [(from, 0.), (to, 1.)].map(|(vertex, position)| {
diff --git a/crates/fj-kernel/src/iter.rs b/crates/fj-kernel/src/iter.rs
index 61d91aa1d..b3bbc65ac 100644
--- a/crates/fj-kernel/src/iter.rs
+++ b/crates/fj-kernel/src/iter.rs
@@ -363,10 +363,10 @@ mod tests {
         builder::{CurveBuilder, CycleBuilder, FaceBuilder, HalfEdgeBuilder},
         insert::Insert,
         objects::{
-            Curve, Cycle, Face, GlobalCurve, GlobalVertex, HalfEdge, Objects,
-            Shell, Sketch, Solid, SurfaceVertex, Vertex,
+            Cycle, Face, GlobalCurve, GlobalVertex, HalfEdge, Objects, Shell,
+            Sketch, Solid, SurfaceVertex, Vertex,
         },
-        partial::HasPartial,
+        partial::{HasPartial, PartialCurve},
     };
 
     use super::ObjectIters as _;
@@ -376,11 +376,13 @@ mod tests {
         let objects = Objects::new();
 
         let surface = objects.surfaces.xy_plane();
-        let object = Curve::partial()
-            .with_surface(Some(surface))
-            .update_as_u_axis()
-            .build(&objects)?
-            .insert(&objects)?;
+        let object = PartialCurve {
+            surface: Some(surface),
+            ..Default::default()
+        }
+        .update_as_u_axis()
+        .build(&objects)?
+        .insert(&objects)?;
 
         assert_eq!(1, object.curve_iter().count());
         assert_eq!(0, object.cycle_iter().count());
@@ -616,11 +618,13 @@ mod tests {
         let objects = Objects::new();
 
         let surface = objects.surfaces.xy_plane();
-        let curve = Curve::partial()
-            .with_surface(Some(surface.clone()))
-            .update_as_u_axis()
-            .build(&objects)?
-            .insert(&objects)?;
+        let curve = PartialCurve {
+            surface: Some(surface.clone()),
+            ..Default::default()
+        }
+        .update_as_u_axis()
+        .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/objects/curve.rs b/crates/fj-kernel/src/partial/objects/curve.rs
index 3a6b3986b..846438a8a 100644
--- a/crates/fj-kernel/src/partial/objects/curve.rs
+++ b/crates/fj-kernel/src/partial/objects/curve.rs
@@ -22,14 +22,6 @@ pub struct PartialCurve {
 }
 
 impl PartialCurve {
-    /// Provide a surface for the partial curve
-    pub fn with_surface(mut self, surface: Option<Handle<Surface>>) -> Self {
-        if let Some(surface) = surface {
-            self.surface = Some(surface);
-        }
-        self
-    }
-
     /// Provide a global form for the partial curve
     pub fn with_global_form(
         mut self,
diff --git a/crates/fj-kernel/src/partial/objects/edge.rs b/crates/fj-kernel/src/partial/objects/edge.rs
index 40e32906e..aaaf6d33a 100644
--- a/crates/fj-kernel/src/partial/objects/edge.rs
+++ b/crates/fj-kernel/src/partial/objects/edge.rs
@@ -48,9 +48,10 @@ impl PartialHalfEdge {
 
     /// Update the partial half-edge with the given surface
     pub fn with_surface(mut self, surface: Handle<Surface>) -> Self {
-        self.curve = self
-            .curve
-            .update_partial(|curve| curve.with_surface(Some(surface.clone())));
+        self.curve = self.curve.update_partial(|mut curve| {
+            curve.surface = Some(surface.clone());
+            curve
+        });
 
         self.vertices = self.vertices.map(|vertex| {
             vertex.update_partial(|vertex| {
diff --git a/crates/fj-kernel/src/validate/vertex.rs b/crates/fj-kernel/src/validate/vertex.rs
index 0ef103fe9..2d04eab55 100644
--- a/crates/fj-kernel/src/validate/vertex.rs
+++ b/crates/fj-kernel/src/validate/vertex.rs
@@ -181,8 +181,8 @@ mod tests {
     use crate::{
         builder::{CurveBuilder, SurfaceVertexBuilder},
         insert::Insert,
-        objects::{Curve, GlobalVertex, Objects, SurfaceVertex, Vertex},
-        partial::HasPartial,
+        objects::{GlobalVertex, Objects, SurfaceVertex, Vertex},
+        partial::{HasPartial, PartialCurve},
         validate::Validate,
     };
 
@@ -193,9 +193,11 @@ mod tests {
         let valid = Vertex::partial()
             .with_position(Some([0.]))
             .with_curve(
-                Curve::partial()
-                    .with_surface(Some(objects.surfaces.xy_plane()))
-                    .update_as_u_axis(),
+                PartialCurve {
+                    surface: Some(objects.surfaces.xy_plane()),
+                    ..Default::default()
+                }
+                .update_as_u_axis(),
             )
             .build(&objects)?;
         let invalid = Vertex::new(
@@ -222,9 +224,11 @@ mod tests {
         let valid = Vertex::partial()
             .with_position(Some([0.]))
             .with_curve(
-                Curve::partial()
-                    .with_surface(Some(objects.surfaces.xy_plane()))
-                    .update_as_u_axis(),
+                PartialCurve {
+                    surface: Some(objects.surfaces.xy_plane()),
+                    ..Default::default()
+                }
+                .update_as_u_axis(),
             )
             .build(&objects)?;
         let invalid = Vertex::new(