diff --git a/tokio-xmpp/src/client/async_client.rs b/tokio-xmpp/src/client/async_client.rs
index ff057df8..cb0f17f2 100644
--- a/tokio-xmpp/src/client/async_client.rs
+++ b/tokio-xmpp/src/client/async_client.rs
@@ -243,42 +243,50 @@ impl Stream for Client {
                 };
 
                 // Poll stream
-                match Pin::new(&mut stream).poll_next(cx) {
-                    Poll::Ready(None) => {
-                        // EOF
-                        self.state = ClientState::Disconnected;
-                        Poll::Ready(Some(Event::Disconnected(Error::Disconnected)))
-                    }
-                    Poll::Ready(Some(Ok(Packet::Stanza(stanza)))) => {
-                        // Receive stanza
-                        self.state = ClientState::Connected(stream);
-                        Poll::Ready(Some(Event::Stanza(stanza)))
-                    }
-                    Poll::Ready(Some(Ok(Packet::Text(_)))) => {
-                        // Ignore text between stanzas
-                        self.state = ClientState::Connected(stream);
-                        Poll::Pending
-                    }
-                    Poll::Ready(Some(Ok(Packet::StreamStart(_)))) => {
-                        // <stream:stream>
-                        self.state = ClientState::Disconnected;
-                        Poll::Ready(Some(Event::Disconnected(
-                            ProtocolError::InvalidStreamStart.into(),
-                        )))
-                    }
-                    Poll::Ready(Some(Ok(Packet::StreamEnd))) => {
-                        // End of stream: </stream:stream>
-                        self.state = ClientState::Disconnected;
-                        Poll::Ready(Some(Event::Disconnected(Error::Disconnected)))
-                    }
-                    Poll::Pending => {
-                        // Try again later
-                        self.state = ClientState::Connected(stream);
-                        Poll::Pending
-                    }
-                    Poll::Ready(Some(Err(e))) => {
-                        self.state = ClientState::Disconnected;
-                        Poll::Ready(Some(Event::Disconnected(e.into())))
+                //
+                // This needs to be a loop in order to ignore packets we don’t care about, or those
+                // we want to handle elsewhere.  Returning something isn’t correct in those two
+                // cases because it would signal to tokio that the XMPPStream is also done, while
+                // there could be additional packets waiting for us.
+                //
+                // The proper solution is thus a loop which we exit once we have something to
+                // return.
+                loop {
+                    match Pin::new(&mut stream).poll_next(cx) {
+                        Poll::Ready(None) => {
+                            // EOF
+                            self.state = ClientState::Disconnected;
+                            return Poll::Ready(Some(Event::Disconnected(Error::Disconnected)));
+                        }
+                        Poll::Ready(Some(Ok(Packet::Stanza(stanza)))) => {
+                            // Receive stanza
+                            self.state = ClientState::Connected(stream);
+                            return Poll::Ready(Some(Event::Stanza(stanza)));
+                        }
+                        Poll::Ready(Some(Ok(Packet::Text(_)))) => {
+                            // Ignore text between stanzas
+                        }
+                        Poll::Ready(Some(Ok(Packet::StreamStart(_)))) => {
+                            // <stream:stream>
+                            self.state = ClientState::Disconnected;
+                            return Poll::Ready(Some(Event::Disconnected(
+                                ProtocolError::InvalidStreamStart.into(),
+                            )));
+                        }
+                        Poll::Ready(Some(Ok(Packet::StreamEnd))) => {
+                            // End of stream: </stream:stream>
+                            self.state = ClientState::Disconnected;
+                            return Poll::Ready(Some(Event::Disconnected(Error::Disconnected)));
+                        }
+                        Poll::Pending => {
+                            // Try again later
+                            self.state = ClientState::Connected(stream);
+                            return Poll::Pending;
+                        }
+                        Poll::Ready(Some(Err(e))) => {
+                            self.state = ClientState::Disconnected;
+                            return Poll::Ready(Some(Event::Disconnected(e.into())));
+                        }
                     }
                 }
             }