diff --git a/tests/client.rs b/tests/client.rs
index 6c9d3d7587..89b90796e0 100644
--- a/tests/client.rs
+++ b/tests/client.rs
@@ -2122,6 +2122,82 @@ mod conn {
             .expect_err("client should be closed");
     }
 
+    #[tokio::test(flavor = "multi_thread", worker_threads = 2)]
+    async fn http2_connect_detect_close() {
+        // Regression test for failure to fully close connections when using HTTP2 CONNECT
+        // We send 2 requests and then drop them. We should see the connection gracefully close.
+        use futures_util::future;
+        let (listener, addr) = setup_tk_test_server().await;
+        let (tx, rxx) = oneshot::channel::<()>();
+
+        tokio::task::spawn(async move {
+            use hyper::server::conn::http2;
+            use hyper::service::service_fn;
+
+            let res = listener.accept().await;
+            let (stream, _) = res.unwrap();
+            let stream = TokioIo::new(stream);
+
+            let service = service_fn(move |req: Request<hyper::body::Incoming>| {
+                tokio::task::spawn(async move {
+                    let io = &mut TokioIo::new(hyper::upgrade::on(req).await.unwrap());
+                    io.write_all(b"hello\n").await.unwrap();
+                });
+
+                future::ok::<_, hyper::Error>(Response::new(Empty::<Bytes>::new()))
+            });
+
+            tokio::task::spawn(async move {
+                let conn = http2::Builder::new(TokioExecutor).serve_connection(stream, service);
+                let _ = conn.await;
+                tx.send(()).unwrap();
+            });
+        });
+
+        let io = tcp_connect(&addr).await.expect("tcp connect");
+        let (mut client, conn) = conn::http2::Builder::new(TokioExecutor)
+            .handshake(io)
+            .await
+            .expect("http handshake");
+
+        tokio::task::spawn(async move {
+            conn.await.expect("client conn");
+        });
+
+        // Sanity check that client is ready
+        future::poll_fn(|ctx| client.poll_ready(ctx))
+            .await
+            .expect("client poll ready sanity");
+        let requests = 2;
+        let mut clients = vec![client.clone(), client];
+        let (tx, rx) = oneshot::channel::<()>();
+        let (tx2, rx2) = oneshot::channel::<()>();
+        let mut rxs = vec![rx, rx2];
+        for _i in 0..requests {
+            let mut client = clients.pop().unwrap();
+            let rx = rxs.pop().unwrap();
+            let req = Request::builder()
+                .method(Method::CONNECT)
+                .uri(format!("{}", addr))
+                .body(Empty::<Bytes>::new())
+                .expect("request builder");
+
+            let resp = client.send_request(req).await.expect("req1 send");
+            assert_eq!(resp.status(), 200);
+            let upgrade = hyper::upgrade::on(resp).await.unwrap();
+            tokio::task::spawn(async move {
+                let _ = rx.await;
+                drop(upgrade);
+            });
+        }
+        drop(tx);
+        drop(tx2);
+        tokio::time::timeout(Duration::from_secs(1), rxx)
+            .await
+            .expect("drop with 1s")
+            .expect("tx dropped without sending");
+    }
+
     #[tokio::test]
     async fn http2_keep_alive_detects_unresponsive_server() {
         let (listener, addr) = setup_tk_test_server().await;