diff --git a/src/core/alive.rs b/src/core/alive.rs
index 5414f0c..1c1b0a1 100644
--- a/src/core/alive.rs
+++ b/src/core/alive.rs
@@ -115,11 +115,12 @@ impl AliveTracker {
     /// during graceful shutdown (tasks that didn't stop within grace period).
     pub async fn snapshot(&self) -> Vec<String> {
         let state = self.state.read().await;
-        let alive: Vec<String> = state
+        let mut alive: Vec<String> = state
             .iter()
             .filter(|(_, ts)| ts.alive)
             .map(|(name, _)| name.clone())
             .collect();
+        alive.sort_unstable();
         alive
     }
 
diff --git a/src/core/registry.rs b/src/core/registry.rs
index 5e34b09..3c4b048 100644
--- a/src/core/registry.rs
+++ b/src/core/registry.rs
@@ -177,16 +177,15 @@ impl Registry {
     /// Spawns an actor and registers its handle.
     async fn spawn_and_register(&self, spec: TaskSpec) {
         let task_name = spec.task().name().to_string();
-        {
-            let tasks = self.tasks.read().await;
-            if tasks.contains_key(&task_name) {
-                self.bus.publish(
-                    Event::new(EventKind::TaskFailed)
-                        .with_task(task_name)
-                        .with_reason("task_already_exists"),
-                );
-                return;
-            }
+
+        let mut tasks = self.tasks.write().await;
+        if tasks.contains_key(&task_name) {
+            self.bus.publish(
+                Event::new(EventKind::TaskFailed)
+                    .with_task(task_name)
+                    .with_reason("task_already_exists"),
+            );
+            return;
         }
 
         let task_token = self.runtime_token.child_token();
@@ -210,23 +209,14 @@ impl Registry {
             cancel: task_token,
         };
 
-        let mut tasks = self.tasks.write().await;
         let was_empty = tasks.is_empty();
-        let inserted = tasks.insert(task_name.clone(), handle).is_none();
+        tasks.insert(task_name.clone(), handle);
         let len_after = tasks.len();
         drop(tasks);
 
-        if inserted {
-            self.notify_after_insert(was_empty, len_after);
-            self.bus
-                .publish(Event::new(EventKind::TaskAdded).with_task(task_name));
-        } else {
-            self.bus.publish(
-                Event::new(EventKind::TaskFailed)
-                    .with_task(task_name)
-                    .with_reason("task_already_exists_race"),
-            );
-        }
+        self.notify_after_insert(was_empty, len_after);
+        self.bus
+            .publish(Event::new(EventKind::TaskAdded).with_task(task_name));
     }
 
     /// Removes a task and cancels its token.
diff --git a/src/core/supervisor.rs b/src/core/supervisor.rs
index 49e1b5e..5b77975 100644
--- a/src/core/supervisor.rs
+++ b/src/core/supervisor.rs
@@ -390,50 +390,38 @@ impl Supervisor {
         wait_for: Duration,
     ) -> Result<bool, RuntimeError> {
         let target = name.to_string();
-        let start = tokio::time::Instant::now();
-        let mut last_poll = tokio::time::Instant::now();
-        let poll_interval = Duration::from_millis(100);
-
-        loop {
-            if start.elapsed() >= wait_for {
-                return Err(RuntimeError::TaskRemoveTimeout {
-                    name: target,
-                    timeout: wait_for,
-                });
-            }
-            if last_poll.elapsed() >= poll_interval {
-                let tasks = self.registry.list().await;
-                if !tasks.contains(&target) {
-                    return Ok(true);
-                }
-                last_poll = tokio::time::Instant::now();
-            }
-
-            let recv_timeout = poll_interval
-                .checked_sub(last_poll.elapsed())
-                .unwrap_or(Duration::from_millis(10));
 
-            match tokio::time::timeout(recv_timeout, rx.recv()).await {
-                Ok(Ok(ev))
-                    if matches!(ev.kind, EventKind::TaskRemoved)
-                        && ev.task.as_deref() == Some(&target) =>
-                {
-                    return Ok(true);
-                }
-                Ok(Ok(_)) => {}
-                Ok(Err(broadcast::error::RecvError::Closed)) => {
-                    let tasks = self.registry.list().await;
-                    return Ok(!tasks.contains(&target));
-                }
-                Ok(Err(broadcast::error::RecvError::Lagged(_))) => {
-                    let tasks = self.registry.list().await;
-                    if !tasks.contains(&target) {
+        let wait_for_event = async {
+            loop {
+                match rx.recv().await {
+                    Ok(ev)
+                        if matches!(ev.kind, EventKind::TaskRemoved)
+                            && ev.task.as_deref() == Some(target.as_str()) =>
+                    {
                         return Ok(true);
                     }
-                    last_poll = tokio::time::Instant::now();
+                    Ok(_) => {}
+                    Err(broadcast::error::RecvError::Lagged(_)) => {
+                        // We may have missed the TaskRemoved event; check the registry.
+                        let tasks = self.registry.list().await;
+                        if !tasks.contains(&target) {
+                            return Ok(true);
+                        }
+                    }
+                    Err(broadcast::error::RecvError::Closed) => {
+                        let tasks = self.registry.list().await;
+                        return Ok(!tasks.contains(&target));
+                    }
                 }
-                Err(_elapsed) => {}
             }
+        };
+
+        match timeout(wait_for, wait_for_event).await {
+            Ok(result) => result,
+            Err(_) => Err(RuntimeError::TaskRemoveTimeout {
+                name: target,
+                timeout: wait_for,
+            }),
         }
     }
 }