diff --git a/compiler/rustc_data_structures/src/sso/set.rs b/compiler/rustc_data_structures/src/sso/set.rs
index f71522d37148a..4fda3adb7b878 100644
--- a/compiler/rustc_data_structures/src/sso/set.rs
+++ b/compiler/rustc_data_structures/src/sso/set.rs
@@ -126,9 +126,10 @@ impl<T: Eq + Hash> SsoHashSet<T> {
 
     /// Adds a value to the set.
     ///
-    /// If the set did not have this value present, `true` is returned.
+    /// Returns whether the value was newly inserted. That is:
     ///
-    /// If the set did have this value present, `false` is returned.
+    /// - If the set did not previously contain this value, `true` is returned.
+    /// - If the set already contained this value, `false` is returned.
     #[inline]
     pub fn insert(&mut self, elem: T) -> bool {
         self.map.insert(elem, ()).is_none()
diff --git a/library/alloc/src/collections/btree/set.rs b/library/alloc/src/collections/btree/set.rs
index 20ef834eaeef3..caa629cf4e65e 100644
--- a/library/alloc/src/collections/btree/set.rs
+++ b/library/alloc/src/collections/btree/set.rs
@@ -770,10 +770,14 @@ impl<T> BTreeSet<T> {
 
     /// Adds a value to the set.
     ///
-    /// If the set did not have an equal element present, `true` is returned.
+    /// Returns whether the value was newly inserted. That is:
     ///
-    /// If the set did have an equal element present, `false` is returned, and
-    /// the entry is not updated. See the [module-level documentation] for more.
+    /// - If the set did not previously contain an equal value, `true` is
+    ///   returned.
+    /// - If the set already contained an equal value, `false` is returned, and
+    ///   the entry is not updated.
+    ///
+    /// See the [module-level documentation] for more.
     ///
     /// [module-level documentation]: index.html#insert-and-complex-keys
     ///
diff --git a/library/std/src/collections/hash/set.rs b/library/std/src/collections/hash/set.rs
index da0572047eca8..19428fe9a2339 100644
--- a/library/std/src/collections/hash/set.rs
+++ b/library/std/src/collections/hash/set.rs
@@ -858,9 +858,10 @@ where
 
     /// Adds a value to the set.
     ///
-    /// If the set did not have this value present, `true` is returned.
+    /// Returns whether the value was newly inserted. That is:
     ///
-    /// If the set did have this value present, `false` is returned.
+    /// - If the set did not previously contain this value, `true` is returned.
+    /// - If the set already contained this value, `false` is returned.
     ///
     /// # Examples
     ///