diff --git a/tests/client.rs b/tests/client.rs
index e4c8d12cf6..73ab121ff0 100644
--- a/tests/client.rs
+++ b/tests/client.rs
@@ -3345,6 +3345,127 @@ mod conn {
         let _ = tokio::time::timeout(Duration::from_secs(5), a_handle).await;
     }
 
+    #[tokio::test]
+    async fn h2_body_progresses_with_peer_window_below_one_kibibyte() {
+        let (client_io, server_io, _) = setup_duplex_test_server();
+        let (headers_tx, headers_rx) = oneshot::channel();
+        let (first_tx, first_rx) = oneshot::channel();
+        tokio::spawn(async move {
+            let mut builder = h2::server::Builder::new();
+            builder.initial_window_size(512);
+            let mut server = builder.handshake::<_, Bytes>(server_io).await.unwrap();
+            let (request, _respond) = server.accept().await.unwrap().unwrap();
+            tokio::spawn(async move {
+                let _ = poll_fn(|cx| server.poll_closed(cx)).await;
+            });
+            headers_tx.send(()).unwrap();
+            let mut body = request.into_body();
+            let first = body.data().await.unwrap().unwrap();
+            first_tx.send(first.len()).unwrap();
+        });
+
+        let io = TokioIo::new(client_io);
+        let (mut client, connection) = conn::http2::Builder::new(TokioExecutor)
+            .handshake::<_, BoxBody<Bytes, Box<dyn Error + Send + Sync>>>(io)
+            .await
+            .expect("http handshake");
+        tokio::spawn(async move {
+            let _ = connection.await;
+        });
+
+        let (mut tx, rx) = mpsc::channel::<Result<Frame<Bytes>, Box<dyn Error + Send + Sync>>>(1);
+        let request = Request::post("http://localhost/small-window")
+            .body(BodyExt::boxed(StreamBody::new(rx)))
+            .unwrap();
+        tokio::spawn(client.send_request(request));
+        headers_rx.await.unwrap();
+
+        use futures_util::SinkExt;
+        tx.send(Ok(Frame::data(Bytes::from(vec![0; 2048]))))
+            .await
+            .unwrap();
+        let first = tokio::time::timeout(Duration::from_secs(5), first_rx)
+            .await
+            .expect("a legal 512-byte stream window must permit DATA progress")
+            .unwrap();
+        assert_eq!(first, 512);
+    }
+
+    #[tokio::test]
+    async fn h2_body_uses_the_last_byte_of_connection_capacity() {
+        const STREAM_A_LEN: usize = 65534;
+
+        let (client_io, server_io, _) = setup_duplex_test_server();
+        let (a_full_tx, a_full_rx) = oneshot::channel();
+        let (b_first_tx, b_first_rx) = oneshot::channel();
+        tokio::spawn(async move {
+            let mut server = h2::server::Builder::new()
+                .handshake::<_, Bytes>(server_io)
+                .await
+                .unwrap();
+            let (a, respond_a) = server.accept().await.unwrap().unwrap();
+            tokio::spawn(async move {
+                let _respond_a = respond_a;
+                let mut body = a.into_body();
+                let mut received = 0;
+                while received < STREAM_A_LEN {
+                    received += body.data().await.unwrap().unwrap().len();
+                }
+                a_full_tx.send(()).unwrap();
+                std::future::pending::<()>().await;
+            });
+            let (b, _respond_b) = server.accept().await.unwrap().unwrap();
+            tokio::spawn(async move {
+                let _ = poll_fn(|cx| server.poll_closed(cx)).await;
+            });
+            let mut body = b.into_body();
+            let first = body.data().await.unwrap().unwrap();
+            b_first_tx.send(first.len()).unwrap();
+        });
+
+        let io = TokioIo::new(client_io);
+        let (mut client, connection) = conn::http2::Builder::new(TokioExecutor)
+            .handshake::<_, BoxBody<Bytes, Box<dyn Error + Send + Sync>>>(io)
+            .await
+            .expect("http handshake");
+        tokio::spawn(async move {
+            let _ = connection.await;
+        });
+
+        let (mut a_tx, a_rx) =
+            mpsc::channel::<Result<Frame<Bytes>, Box<dyn Error + Send + Sync>>>(4);
+        let mut client_a = client.clone();
+        tokio::spawn(async move {
+            let request = Request::post("http://localhost/a")
+                .body(BodyExt::boxed(StreamBody::new(a_rx)))
+                .unwrap();
+            let _ = client_a.send_request(request).await;
+        });
+        use futures_util::SinkExt;
+        let mut remaining = STREAM_A_LEN;
+        while remaining != 0 {
+            let len = remaining.min(16_384);
+            a_tx.send(Ok(Frame::data(Bytes::from(vec![0; len]))))
+                .await
+                .unwrap();
+            remaining -= len;
+        }
+        a_full_rx.await.unwrap();
+
+        let request = Request::post("http://localhost/b")
+            .body(BodyExt::boxed(
+                Full::new(Bytes::from(vec![0; 10_000]))
+                    .map_err(|never: std::convert::Infallible| match never {}),
+            ))
+            .unwrap();
+        tokio::spawn(client.send_request(request));
+        let first = tokio::time::timeout(Duration::from_secs(5), b_first_rx)
+            .await
+            .expect("the final connection byte must be usable without a WINDOW_UPDATE")
+            .unwrap();
+        assert_eq!(first, 1);
+    }
+
     // https://github.com/hyperium/hyper/issues/4003, for HTTP/2 CONNECT
     //
     // Like `h2_idle_stream_does_not_pin_connection_window`, but the idle