diff --git a/swarm/CHANGELOG.md b/swarm/CHANGELOG.md
index b5578f90a38..c7cc8c23520 100644
--- a/swarm/CHANGELOG.md
+++ b/swarm/CHANGELOG.md
@@ -6,6 +6,11 @@
 - Raise MSRV to 1.88.0.
   See [PR 6273](https://github.com/libp2p/rust-libp2p/pull/6273).
 
+- Fix `panic!("cannot extract twice")` in `Connection::poll` by selecting
+  a `Waiting` `SubstreamRequested` explicitly instead of the first entry,
+  which could be a stale `Done` left behind by a prior extraction.
+  See [PR 6427](https://github.com/libp2p/rust-libp2p/pull/6427).
+
 ## 0.47.1
 
 - Replace `lru::LruCache` with `hashlink::LruCache`.
diff --git a/swarm/src/connection.rs b/swarm/src/connection.rs
index 0a1a634d8b8..dffb93e197b 100644
--- a/swarm/src/connection.rs
+++ b/swarm/src/connection.rs
@@ -411,12 +411,13 @@ where
                 }
             }
 
-            if let Some(requested_substream) = requested_substreams.iter_mut().next() {
-                match muxing.poll_outbound_unpin(cx)? {
-                    Poll::Pending => {}
-                    Poll::Ready(substream) => {
-                        let (user_data, timeout, upgrade) = requested_substream.extract();
-
+            match muxing.poll_outbound_unpin(cx)? {
+                Poll::Pending => {}
+                Poll::Ready(substream) => {
+                    if let Some((user_data, timeout, upgrade)) = requested_substreams
+                        .iter_mut()
+                        .find_map(SubstreamRequested::extract)
+                    {
                         negotiating_out.push(StreamUpgrade::new_outbound(
                             substream,
                             user_data,
@@ -425,11 +426,11 @@ where
                             *substream_upgrade_protocol_override,
                             stream_counter.clone(),
                         ));
-
-                        // Go back to the top,
-                        // handler can potentially make progress again.
-                        continue;
                     }
+
+                    // Go back to the top,
+                    // handler can potentially make progress again.
+                    continue;
                 }
             }
 
@@ -691,7 +692,7 @@ impl<UserData, Upgrade> SubstreamRequested<UserData, Upgrade> {
         }
     }
 
-    fn extract(&mut self) -> (UserData, Delay, Upgrade) {
+    fn extract(&mut self) -> Option<(UserData, Delay, Upgrade)> {
         match mem::replace(self, Self::Done) {
             SubstreamRequested::Waiting {
                 user_data,
@@ -703,9 +704,9 @@ impl<UserData, Upgrade> SubstreamRequested<UserData, Upgrade> {
                     waker.wake();
                 }
 
-                (user_data, timeout, upgrade)
+                Some((user_data, timeout, upgrade))
             }
-            SubstreamRequested::Done => panic!("cannot extract twice"),
+            SubstreamRequested::Done => None,
         }
     }
 }
@@ -855,6 +856,23 @@ mod tests {
         ))
     }
 
+    /// Regression test for "cannot extract twice".
+    #[test]
+    fn connection_poll_skips_done_substream_requested_entries() {
+        let mut connection = Connection::new(
+            StreamMuxerBox::new(ReadyOutboundStreamMuxer { remaining: 2 }),
+            MockConnectionHandler::new(Duration::from_secs(10)),
+            None,
+            0,
+            Duration::ZERO,
+        );
+
+        connection.handler.open_outbound_substreams(2);
+
+        let _ = connection.poll_noop_waker();
+        let _ = connection.poll_noop_waker();
+    }
+
     #[test]
     fn propagates_changes_to_supported_inbound_protocols() {
         let mut connection = Connection::new(
@@ -1098,6 +1116,47 @@ mod tests {
         }
     }
 
+    /// A [`StreamMuxer`] which immediately returns outbound streams.
+    struct ReadyOutboundStreamMuxer {
+        remaining: usize,
+    }
+
+    impl StreamMuxer for ReadyOutboundStreamMuxer {
+        type Substream = PendingSubstream;
+        type Error = Infallible;
+
+        fn poll_inbound(
+            self: Pin<&mut Self>,
+            _: &mut Context<'_>,
+        ) -> Poll<Result<Self::Substream, Self::Error>> {
+            Poll::Pending
+        }
+
+        fn poll_outbound(
+            mut self: Pin<&mut Self>,
+            _: &mut Context<'_>,
+        ) -> Poll<Result<Self::Substream, Self::Error>> {
+            if self.remaining == 0 {
+                return Poll::Pending;
+            }
+
+            self.remaining -= 1;
+
+            Poll::Ready(Ok(PendingSubstream { _weak: Weak::new() }))
+        }
+
+        fn poll_close(self: Pin<&mut Self>, _: &mut Context<'_>) -> Poll<Result<(), Self::Error>> {
+            Poll::Pending
+        }
+
+        fn poll(
+            self: Pin<&mut Self>,
+            _: &mut Context<'_>,
+        ) -> Poll<Result<StreamMuxerEvent, Self::Error>> {
+            Poll::Pending
+        }
+    }
+
     struct PendingSubstream {
         _weak: Weak<()>,
     }
@@ -1131,7 +1190,7 @@ mod tests {
     }
 
     struct MockConnectionHandler {
-        outbound_requested: bool,
+        outbound_requested: usize,
         error: Option<StreamUpgradeError<Infallible>>,
         upgrade_timeout: Duration,
     }
@@ -1139,14 +1198,18 @@ mod tests {
     impl MockConnectionHandler {
         fn new(upgrade_timeout: Duration) -> Self {
             Self {
-                outbound_requested: false,
+                outbound_requested: 0,
                 error: None,
                 upgrade_timeout,
             }
         }
 
         fn open_new_outbound(&mut self) {
-            self.outbound_requested = true;
+            self.open_outbound_substreams(1);
+        }
+
+        fn open_outbound_substreams(&mut self, count: usize) {
+            self.outbound_requested += count;
         }
     }
 
@@ -1231,8 +1294,8 @@ mod tests {
             &mut self,
             _: &mut Context<'_>,
         ) -> Poll<ConnectionHandlerEvent<Self::OutboundProtocol, (), Self::ToBehaviour>> {
-            if self.outbound_requested {
-                self.outbound_requested = false;
+            if self.outbound_requested > 0 {
+                self.outbound_requested -= 1;
                 return Poll::Ready(ConnectionHandlerEvent::OutboundSubstreamRequest {
                     protocol: SubstreamProtocol::new(DeniedUpgrade, ())
                         .with_timeout(self.upgrade_timeout),