diff --git a/library/alloc/src/rc.rs b/library/alloc/src/rc.rs
index 6b4b5f790004..619d9f258e34 100644
--- a/library/alloc/src/rc.rs
+++ b/library/alloc/src/rc.rs
@@ -1331,7 +1331,7 @@ impl<T: ?Sized> Rc<T> {
     /// same layout requirements specified in [`Rc::from_raw_in`][from_raw_in].
     /// The associated `Rc` instance must be valid (i.e. the strong count must be at
     /// least 1) for the duration of this method, and `ptr` must point to a block of memory
-    /// allocated by `alloc`.
+    /// allocated by the global allocator.
     ///
     /// [from_raw_in]: Rc::from_raw_in
     ///
@@ -1678,7 +1678,7 @@ impl<T: ?Sized, A: Allocator> Rc<T, A> {
     /// same layout requirements specified in [`Rc::from_raw_in`][from_raw_in].
     /// The associated `Rc` instance must be valid (i.e. the strong count must be at
     /// least 1) when invoking this method, and `ptr` must point to a block of memory
-    /// allocated by the global allocator. This method can be used to release the final `Rc` and
+    /// allocated by `alloc`. This method can be used to release the final `Rc` and
     /// backing storage, but **should not** be called after the final `Rc` has been released.
     ///
     /// [from_raw_in]: Rc::from_raw_in
diff --git a/library/alloc/src/sync.rs b/library/alloc/src/sync.rs
index 6bb037c57deb..104cb35c23b6 100644
--- a/library/alloc/src/sync.rs
+++ b/library/alloc/src/sync.rs
@@ -1816,7 +1816,7 @@ impl<T: ?Sized, A: Allocator> Arc<T, A> {
     /// same layout requirements specified in [`Arc::from_raw_in`][from_raw_in].
     /// The associated `Arc` instance must be valid (i.e. the strong count must be at
     /// least 1) for the duration of this method, and `ptr` must point to a block of memory
-    /// allocated by the global allocator.
+    /// allocated by `alloc`.
     ///
     /// [from_raw_in]: Arc::from_raw_in
     ///
@@ -1863,7 +1863,7 @@ impl<T: ?Sized, A: Allocator> Arc<T, A> {
     /// same layout requirements specified in [`Arc::from_raw_in`][from_raw_in].
     /// The associated `Arc` instance must be valid (i.e. the strong count must be at
     /// least 1) when invoking this method, and `ptr` must point to a block of memory
-    /// allocated by the global allocator. This method can be used to release the final
+    /// allocated by `alloc`. This method can be used to release the final
     /// `Arc` and backing storage, but **should not** be called after the final `Arc` has been
     /// released.
     ///