diff --git a/tokio/tests/rt_common.rs b/tokio/tests/rt_common.rs
index 58df53f0170..f5dce54d879 100644
--- a/tokio/tests/rt_common.rs
+++ b/tokio/tests/rt_common.rs
@@ -950,10 +950,6 @@ rt_test! {
     #[test]
     fn wake_while_rt_is_dropping() {
         use tokio::sync::Barrier;
-        use core::sync::atomic::{AtomicBool, Ordering};
-
-        let drop_triggered = Arc::new(AtomicBool::new(false));
-        let set_drop_triggered = drop_triggered.clone();
 
         struct OnDrop<F: FnMut()>(F);
 
@@ -965,56 +961,39 @@ rt_test! {
 
         let (tx1, rx1) = oneshot::channel();
         let (tx2, rx2) = oneshot::channel();
-        let (tx3, rx3) = oneshot::channel();
 
-        let barrier = Arc::new(Barrier::new(4));
+        let barrier = Arc::new(Barrier::new(3));
         let barrier1 = barrier.clone();
         let barrier2 = barrier.clone();
-        let barrier3 = barrier.clone();
 
         let rt = rt();
 
         rt.spawn(async move {
+            let mut tx2 = Some(tx2);
+            let _d = OnDrop(move || {
+                let _ = tx2.take().unwrap().send(());
+            });
+
             // Ensure a waker gets stored in oneshot 1.
             let _ = tokio::join!(rx1, barrier1.wait());
-            tx3.send(()).unwrap();
         });
 
         rt.spawn(async move {
-            let h1 = tokio::runtime::Handle::current();
-            // When this task is dropped, we'll be "closing remotes".
-            // We spawn a new task that owns the `tx1`, to move its Drop
-            // out of here.
-            //
-            // Importantly, the oneshot 1 has a waker already stored, so
-            // the eventual drop here will try to re-schedule again.
-            let mut opt_tx1 = Some(tx1);
+            let mut tx1 = Some(tx1);
             let _d = OnDrop(move || {
-                let tx1 = opt_tx1.take().unwrap();
-                h1.spawn(async move {
-                    tx1.send(()).unwrap();
-                });
-                // Just a sanity check that this entire thing actually happened
-                set_drop_triggered.store(true, Ordering::Relaxed);
+                let _ = tx1.take().unwrap().send(());
             });
-            let _ = tokio::join!(rx2, barrier2.wait());
-        });
 
-        rt.spawn(async move {
-            let _ = tokio::join!(rx3, barrier3.wait());
-            // We'll never get here, but once task 3 drops, this will
-            // force task 2 to re-schedule since it's waiting on oneshot 2.
-            tx2.send(()).unwrap();
+            // Ensure a waker gets stored in oneshot 2.
+            let _ = tokio::join!(rx2, barrier2.wait());
         });
 
         // Wait until every oneshot channel has been polled.
         rt.block_on(barrier.wait());
 
-        // Drop the rt
+        // Drop the rt. Regardless of which task is dropped first, its destructor will wake the
+        // other task.
         drop(rt);
-
-        // Make sure that the spawn actually happened
-        assert!(drop_triggered.load(Ordering::Relaxed));
     }
 
     #[cfg(not(target_os="wasi"))] // Wasi doesn't support UDP or bind()