diff --git a/src/subsystem/subsystem_handle.rs b/src/subsystem/subsystem_handle.rs
index 702dacc..0cc4c99 100644
--- a/src/subsystem/subsystem_handle.rs
+++ b/src/subsystem/subsystem_handle.rs
@@ -165,7 +165,7 @@ impl<ErrType: ErrTypeTraits> SubsystemHandle<ErrType> {
     }
 
     /// Waits until all the children of this subsystem are finished.
-    pub async fn wait_for_children(&mut self) {
+    pub async fn wait_for_children(&self) {
         self.inner.joiner_token.join_children().await
     }
 
diff --git a/src/utils/joiner_token.rs b/src/utils/joiner_token.rs
index a60ecc5..4973791 100644
--- a/src/utils/joiner_token.rs
+++ b/src/utils/joiner_token.rs
@@ -70,9 +70,7 @@ impl<ErrType: ErrTypeTraits> JoinerToken<ErrType> {
         (Self { inner }, weak_ref)
     }
 
-    // Requires `mut` access to prevent children from being spawned
-    // while waiting
-    pub(crate) async fn join_children(&mut self) {
+    pub(crate) async fn join_children(&self) {
         let mut subscriber = self.inner.counter.subscribe();
 
         // Ignore errors; if the channel got closed, that definitely means
diff --git a/tests/integration_test_2.rs b/tests/integration_test_2.rs
index 9748f58..6510fe3 100644
--- a/tests/integration_test_2.rs
+++ b/tests/integration_test_2.rs
@@ -70,7 +70,7 @@ async fn wait_for_children() {
         BoxedResult::Ok(())
     };
 
-    let subsys1 = move |mut subsys: SubsystemHandle| async move {
+    let subsys1 = move |subsys: SubsystemHandle| async move {
         subsys.start(SubsystemBuilder::new("nested1", nested_subsys1));
 
         sleep(Duration::from_millis(100)).await;
@@ -97,3 +97,64 @@ async fn wait_for_children() {
     .await
     .unwrap();
 }
+
+#[tokio::test]
+#[traced_test]
+async fn request_local_shutdown() {
+    let (nested1_started, set_nested1_started) = Event::create();
+    let (nested1_finished, set_nested1_finished) = Event::create();
+    let (nested2_started, set_nested2_started) = Event::create();
+    let (nested2_finished, set_nested2_finished) = Event::create();
+    let (global_finished, set_global_finished) = Event::create();
+
+    let nested_subsys2 = move |subsys: SubsystemHandle| async move {
+        set_nested2_started();
+        subsys.on_shutdown_requested().await;
+        set_nested2_finished();
+        BoxedResult::Ok(())
+    };
+
+    let nested_subsys1 = move |subsys: SubsystemHandle| async move {
+        subsys.start(SubsystemBuilder::new("nested2", nested_subsys2));
+        set_nested1_started();
+        subsys.on_shutdown_requested().await;
+        set_nested1_finished();
+        BoxedResult::Ok(())
+    };
+
+    let subsys1 = move |subsys: SubsystemHandle| async move {
+        subsys.start(SubsystemBuilder::new("nested1", nested_subsys1));
+
+        sleep(Duration::from_millis(100)).await;
+
+        assert!(nested1_started.get());
+        assert!(!nested1_finished.get());
+        assert!(nested2_started.get());
+        assert!(!nested2_finished.get());
+        assert!(!global_finished.get());
+
+        subsys.request_local_shutdown();
+        sleep(Duration::from_millis(200)).await;
+
+        assert!(nested1_finished.get());
+        assert!(nested2_finished.get());
+        assert!(!global_finished.get());
+
+        subsys.request_shutdown();
+        sleep(Duration::from_millis(50)).await;
+
+        assert!(global_finished.get());
+
+        BoxedResult::Ok(())
+    };
+
+    Toplevel::new(move |s| async move {
+        s.start(SubsystemBuilder::new("subsys", subsys1));
+
+        s.on_shutdown_requested().await;
+        set_global_finished();
+    })
+    .handle_shutdown_requests(Duration::from_millis(100))
+    .await
+    .unwrap();
+}