diff --git a/crates/fj-core/src/algorithms/approx/face.rs b/crates/fj-core/src/algorithms/approx/face.rs
index aedccf6a5..d94372f84 100644
--- a/crates/fj-core/src/algorithms/approx/face.rs
+++ b/crates/fj-core/src/algorithms/approx/face.rs
@@ -7,7 +7,7 @@ use std::{collections::BTreeSet, ops::Deref};
 use fj_interop::mesh::Color;
 
 use crate::{
-    objects::{Face, Handedness, Handles},
+    objects::{Face, Handedness, ObjectSet},
     validate::ValidationConfig,
 };
 
@@ -16,7 +16,7 @@ use super::{
     Tolerance,
 };
 
-impl Approx for &Handles<Face> {
+impl Approx for &ObjectSet<Face> {
     type Approximation = BTreeSet<FaceApprox>;
     type Cache = HalfEdgeApproxCache;
 
diff --git a/crates/fj-core/src/objects/kinds/cycle.rs b/crates/fj-core/src/objects/kinds/cycle.rs
index f8f92db16..61bb4179a 100644
--- a/crates/fj-core/src/objects/kinds/cycle.rs
+++ b/crates/fj-core/src/objects/kinds/cycle.rs
@@ -2,14 +2,14 @@ use fj_math::{Scalar, Winding};
 
 use crate::{
     geometry::SurfacePath,
-    objects::{handles::Handles, HalfEdge},
+    objects::{HalfEdge, ObjectSet},
     storage::Handle,
 };
 
 /// A cycle of connected edges
 #[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct Cycle {
-    half_edges: Handles<HalfEdge>,
+    half_edges: ObjectSet<HalfEdge>,
 }
 
 impl Cycle {
@@ -20,7 +20,7 @@ impl Cycle {
     }
 
     /// Access the edges that make up the cycle
-    pub fn half_edges(&self) -> &Handles<HalfEdge> {
+    pub fn half_edges(&self) -> &ObjectSet<HalfEdge> {
         &self.half_edges
     }
 
diff --git a/crates/fj-core/src/objects/kinds/region.rs b/crates/fj-core/src/objects/kinds/region.rs
index a15cc40cf..4744aa11b 100644
--- a/crates/fj-core/src/objects/kinds/region.rs
+++ b/crates/fj-core/src/objects/kinds/region.rs
@@ -2,7 +2,7 @@
 use fj_interop::mesh::Color;
 
 use crate::{
-    objects::{handles::Handles, Cycle},
+    objects::{Cycle, ObjectSet},
     storage::Handle,
 };
 
@@ -17,7 +17,7 @@ use crate::{
 #[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct Region {
     exterior: Handle<Cycle>,
-    interiors: Handles<Cycle>,
+    interiors: ObjectSet<Cycle>,
     color: Option<Color>,
 }
 
@@ -43,7 +43,7 @@ impl Region {
     /// Access the cycles that bound the region on the inside
     ///
     /// Each of these cycles defines a hole in the region .
-    pub fn interiors(&self) -> &Handles<Cycle> {
+    pub fn interiors(&self) -> &ObjectSet<Cycle> {
         &self.interiors
     }
 
diff --git a/crates/fj-core/src/objects/kinds/shell.rs b/crates/fj-core/src/objects/kinds/shell.rs
index c905cf70b..fd6b8574b 100644
--- a/crates/fj-core/src/objects/kinds/shell.rs
+++ b/crates/fj-core/src/objects/kinds/shell.rs
@@ -1,12 +1,12 @@
 use crate::{
-    objects::{handles::Handles, Face},
+    objects::{Face, ObjectSet},
     storage::Handle,
 };
 
 /// A 3-dimensional closed shell
 #[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct Shell {
-    faces: Handles<Face>,
+    faces: ObjectSet<Face>,
 }
 
 impl Shell {
@@ -18,7 +18,7 @@ impl Shell {
     }
 
     /// Access the faces of the shell
-    pub fn faces(&self) -> &Handles<Face> {
+    pub fn faces(&self) -> &ObjectSet<Face> {
         &self.faces
     }
 }
diff --git a/crates/fj-core/src/objects/kinds/sketch.rs b/crates/fj-core/src/objects/kinds/sketch.rs
index f6d19d22b..5f4a29d60 100644
--- a/crates/fj-core/src/objects/kinds/sketch.rs
+++ b/crates/fj-core/src/objects/kinds/sketch.rs
@@ -1,12 +1,12 @@
 use crate::{
-    objects::{handles::Handles, Region},
+    objects::{ObjectSet, Region},
     storage::Handle,
 };
 
 /// A 2-dimensional shape
 #[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct Sketch {
-    regions: Handles<Region>,
+    regions: ObjectSet<Region>,
 }
 
 impl Sketch {
@@ -18,7 +18,7 @@ impl Sketch {
     }
 
     /// Access the regions of the sketch
-    pub fn regions(&self) -> &Handles<Region> {
+    pub fn regions(&self) -> &ObjectSet<Region> {
         &self.regions
     }
 }
diff --git a/crates/fj-core/src/objects/kinds/solid.rs b/crates/fj-core/src/objects/kinds/solid.rs
index 203ca6189..589c45191 100644
--- a/crates/fj-core/src/objects/kinds/solid.rs
+++ b/crates/fj-core/src/objects/kinds/solid.rs
@@ -1,5 +1,5 @@
 use crate::{
-    objects::{handles::Handles, Shell},
+    objects::{ObjectSet, Shell},
     storage::Handle,
 };
 
@@ -13,7 +13,7 @@ use crate::{
 /// not currently validated.
 #[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
 pub struct Solid {
-    shells: Handles<Shell>,
+    shells: ObjectSet<Shell>,
 }
 
 impl Solid {
@@ -25,7 +25,7 @@ impl Solid {
     }
 
     /// Access the solid's shells
-    pub fn shells(&self) -> &Handles<Shell> {
+    pub fn shells(&self) -> &ObjectSet<Shell> {
         &self.shells
     }
 }
diff --git a/crates/fj-core/src/objects/mod.rs b/crates/fj-core/src/objects/mod.rs
index be6383c04..c4dccaa02 100644
--- a/crates/fj-core/src/objects/mod.rs
+++ b/crates/fj-core/src/objects/mod.rs
@@ -39,13 +39,12 @@
 //!
 //! [`Handle`]: crate::storage::Handle
 
-mod handles;
 mod kinds;
 mod object;
+mod object_set;
 mod stores;
 
 pub use self::{
-    handles::Handles,
     kinds::{
         curve::Curve,
         cycle::Cycle,
@@ -59,5 +58,6 @@ pub use self::{
         vertex::Vertex,
     },
     object::{Bare, BehindHandle, Form, Object, WithHandle},
+    object_set::ObjectSet,
     stores::{Objects, Surfaces},
 };
diff --git a/crates/fj-core/src/objects/handles.rs b/crates/fj-core/src/objects/object_set.rs
similarity index 85%
rename from crates/fj-core/src/objects/handles.rs
rename to crates/fj-core/src/objects/object_set.rs
index 6ebce9b4f..f8928e0d3 100644
--- a/crates/fj-core/src/objects/handles.rs
+++ b/crates/fj-core/src/objects/object_set.rs
@@ -4,27 +4,26 @@ use itertools::Itertools;
 
 use crate::storage::Handle;
 
-/// An ordered set of object handles
+/// An ordered set of objects
 ///
 /// This is the data structure used by all objects that reference multiple
 /// objects of the same type. It is a set, not containing any duplicate
 /// elements, and it maintains the insertion order of those elements.
 #[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
-pub struct Handles<T> {
+pub struct ObjectSet<T> {
     // This is supposed to be a set data structure, so what is that `Vec` doing
     // here? Well, it's here because we need it to preserve insertion order, but
     // that doesn't explain why it is here *alone*.
     //
     // If you look closely, you'll notice that this is an immutable data
     // structure (since it is used in objects, and objects themselves are
-    // immutable). We make sure there are no duplicates when this is
-    // constructed (see the `FromIterator` implementation below), but after
-    // that, we're fine.
+    // immutable). We need to make sure there are no duplicates when this is
+    // constructed (see the constructor below), but after that, we're fine.
     inner: Vec<Handle<T>>,
 }
 
-impl<T> Handles<T> {
-    /// Create a new instances of `Handles` from an iterator over `Handle<T>`
+impl<T> ObjectSet<T> {
+    /// Create an instances of `ObjectSet` from an iterator over `Handle<T>`
     ///
     /// # Panics
     ///
@@ -39,7 +38,7 @@ impl<T> Handles<T> {
         for handle in handles {
             if added.contains(&handle) {
                 panic!(
-                    "Constructing `HandleSet` with duplicate handle: {:?}",
+                    "Constructing `ObjectSet` with duplicate handle: {:?}",
                     handle
                 );
             }
@@ -51,7 +50,7 @@ impl<T> Handles<T> {
         Self { inner }
     }
 
-    /// Return the number of handles in this set
+    /// Return the number of objects in this set
     pub fn len(&self) -> usize {
         self.inner.len()
     }
@@ -103,14 +102,14 @@ impl<T> Handles<T> {
 
     /// Return the n-th item, treating the index space as circular
     ///
-    /// If the length of `Handles` is `i`, then retrieving the i-th edge using
-    /// this method, is the same as retrieving the 0-th one.
+    /// If the length of `ObjectSet` is `i`, then retrieving the i-th edge using
+    /// this method, is the same as retrieving the 0-th one, and so on.
     ///
     /// # Panics
     ///
-    /// Panics, if `Handles` is empty.
+    /// Panics, if `ObjectSet` is empty.
     pub fn nth_circular(&self, index: usize) -> &Handle<T> {
-        assert!(!self.is_empty(), "`Handles` must not be empty");
+        assert!(!self.is_empty(), "`ObjectSet` must not be empty");
 
         let index = index % self.len();
         self.nth(index)
@@ -130,17 +129,17 @@ impl<T> Handles<T> {
             .map(|index| self.nth_circular(index + 1))
     }
 
-    /// Access an iterator over the handles
+    /// Access an iterator over the objects
     pub fn iter(&self) -> slice::Iter<Handle<T>> {
         self.inner.iter()
     }
 
-    /// Return iterator over the pairs of all handles
+    /// Access an iterator over the neighboring pairs of all contained objects
     pub fn pairs(&self) -> impl Iterator<Item = (&Handle<T>, &Handle<T>)> {
         self.iter().circular_tuple_windows()
     }
 
-    /// Create a new instance in which the provided item has been replaced
+    /// Create a new instance in which the provided object has been replaced
     ///
     /// Returns `None`, if the provided item is not present.
     ///
@@ -191,7 +190,7 @@ impl<T> Handles<T> {
     }
 }
 
-impl<O> FromIterator<Handle<O>> for Handles<O>
+impl<O> FromIterator<Handle<O>> for ObjectSet<O>
 where
     O: Debug + Ord,
 {
@@ -200,7 +199,7 @@ where
     }
 }
 
-impl<T> IntoIterator for Handles<T> {
+impl<T> IntoIterator for ObjectSet<T> {
     type Item = Handle<T>;
     type IntoIter = vec::IntoIter<Handle<T>>;
 
@@ -209,7 +208,7 @@ impl<T> IntoIterator for Handles<T> {
     }
 }
 
-impl<'r, T> IntoIterator for &'r Handles<T> {
+impl<'r, T> IntoIterator for &'r ObjectSet<T> {
     // You might wonder why we're returning references to handles here, when
     // `Handle` already is kind of reference, and easily cloned.
     //