diff --git a/swarm/src/lib.rs b/swarm/src/lib.rs
index 6e92aab793b..2af0ca5d215 100644
--- a/swarm/src/lib.rs
+++ b/swarm/src/lib.rs
@@ -681,9 +681,9 @@ where
 /// Notify all of the given connections of a peer of an event.
 ///
 /// Returns `Some` with the given event and a new list of connections if
-/// at least one of the given connections is currently not able to receive
-/// the event, in which case the current task is scheduled to be woken up and
-/// the returned connections are those which still need to receive the event.
+/// at least one of the given connections is not currently able to receive the event
+/// but is not closing, in which case the current task is scheduled to be woken up.
+/// The returned connections are those which are not closing.
 ///
 /// Returns `None` if all connections are either closing or the event
 /// was successfully sent to all handlers whose connections are not closing,
@@ -707,23 +707,26 @@ where
         }
     }
 
-    let mut pending = SmallVec::new();
-    for id in ids.into_iter() {
-        if let Some(mut conn) = peer.connection(id) {
-            match conn.poll_ready_notify_handler(cx) {
-                Poll::Pending => pending.push(id),
-                Poll::Ready(Ok(())) => {
-                    // Can now only fail due to the connection suddenly closing,
-                    // which we ignore.
-                    let _ = conn.notify_handler(event.clone());
-                },
-                Poll::Ready(Err(())) => {} // connection is closing
+    {
+        let mut pending = SmallVec::new();
+        for id in ids.iter() {
+            if let Some(mut conn) = peer.connection(*id) { // (*)
+                if conn.poll_ready_notify_handler(cx).is_pending() {
+                    pending.push(*id)
+                }
             }
         }
+        if !pending.is_empty() {
+            return Some((event, pending))
+        }
     }
 
-    if !pending.is_empty() {
-        return Some((event, pending))
+    for id in ids.into_iter() {
+        if let Some(mut conn) = peer.connection(id) {
+            // All connections were ready. Can now only fail due
+            // to a connection suddenly closing, which we ignore.
+            let _ = conn.notify_handler(event.clone());
+        }
     }
 
     None