diff --git a/tests/_async/test_http2.py b/tests/_async/test_http2.py
index b4ec66488..42542481c 100644
--- a/tests/_async/test_http2.py
+++ b/tests/_async/test_http2.py
@@ -1,8 +1,12 @@
+import time
+
 import hpack
 import hyperframe.frame
 import pytest
+import trio as concurrency
 
 import httpcore
+from tests import h2server
 
 
 @pytest.mark.anyio
@@ -380,3 +384,28 @@ async def test_http2_remote_max_streams_update():
                         conn._h2_state.local_settings.max_concurrent_streams,
                     )
                 i += 1
+
+
+@pytest.mark.trio
+@pytest.mark.xfail(reason="https://github.com/encode/httpx/discussions/3278")
+async def test_slow_overlapping_requests():
+    fetches = []
+
+    with h2server.run() as server:
+        url = f"http://127.0.0.1:{server.port}/"
+
+        async with httpcore.AsyncConnectionPool(http1=False, http2=True) as pool:
+
+            async def fetch(start_delay):
+                await concurrency.sleep(start_delay)
+
+                start = time.time()
+                await pool.request("GET", url)
+                end = time.time()
+                fetches.append(round(end - start, 1))
+
+            async with concurrency.open_nursery() as nursery:
+                for start_delay in [0, 0.2, 0.4, 0.6, 0.8]:
+                    nursery.start_soon(fetch, start_delay)
+
+    assert fetches == [1.0] * 5
diff --git a/tests/_sync/test_http2.py b/tests/_sync/test_http2.py
index 695359bd6..334da3970 100644
--- a/tests/_sync/test_http2.py
+++ b/tests/_sync/test_http2.py
@@ -1,8 +1,12 @@
+import time
+
 import hpack
 import hyperframe.frame
 import pytest
+from tests import concurrency
 
 import httpcore
+from tests import h2server
 
 
 
@@ -380,3 +384,28 @@ def test_http2_remote_max_streams_update():
                         conn._h2_state.local_settings.max_concurrent_streams,
                     )
                 i += 1
+
+
+
+@pytest.mark.xfail(reason="https://github.com/encode/httpx/discussions/3278")
+def test_slow_overlapping_requests():
+    fetches = []
+
+    with h2server.run() as server:
+        url = f"http://127.0.0.1:{server.port}/"
+
+        with httpcore.ConnectionPool(http1=False, http2=True) as pool:
+
+            def fetch(start_delay):
+                concurrency.sleep(start_delay)
+
+                start = time.time()
+                pool.request("GET", url)
+                end = time.time()
+                fetches.append(round(end - start, 1))
+
+            with concurrency.open_nursery() as nursery:
+                for start_delay in [0, 0.2, 0.4, 0.6, 0.8]:
+                    nursery.start_soon(fetch, start_delay)
+
+    assert fetches == [1.0] * 5
diff --git a/tests/concurrency.py b/tests/concurrency.py
index a0572d531..382d206a3 100644
--- a/tests/concurrency.py
+++ b/tests/concurrency.py
@@ -10,6 +10,7 @@
 """
 
 import threading
+import time
 from types import TracebackType
 from typing import Any, Callable, List, Optional, Type
 
@@ -39,3 +40,7 @@ def start_soon(self, func: Callable[..., object], *args: Any) -> None:
 
 def open_nursery() -> Nursery:
     return Nursery()
+
+
+def sleep(seconds: float) -> None:
+    time.sleep(seconds)
diff --git a/tests/h2server.py b/tests/h2server.py
new file mode 100644
index 000000000..6b910c72f
--- /dev/null
+++ b/tests/h2server.py
@@ -0,0 +1,93 @@
+import contextlib
+import logging
+import socket
+import threading
+import time
+
+import h2.config
+import h2.connection
+import h2.events
+
+
+def send_response(sock, conn, event):
+    start = time.time()
+    logging.info("Starting %s.", event)
+
+    time.sleep(1)
+
+    stream_id = event.stream_id
+    conn.send_headers(
+        stream_id=stream_id,
+        headers=[(":status", "200"), ("server", "basic-h2-server/1.0")],
+    )
+    data_to_send = conn.data_to_send()
+    if data_to_send:
+        sock.sendall(data_to_send)
+
+    conn.send_data(stream_id=stream_id, data=b"it works!", end_stream=True)
+    data_to_send = conn.data_to_send()
+    if data_to_send:
+        sock.sendall(data_to_send)
+
+    end = time.time()
+    logging.info("Finished %s in %.03fs.", event, end - start)
+
+
+def handle(sock: socket.socket) -> None:
+    config = h2.config.H2Configuration(client_side=False)
+    conn = h2.connection.H2Connection(config=config)
+    conn.initiate_connection()
+    sock.sendall(conn.data_to_send())
+
+    while True:
+        data = sock.recv(65535)
+        if not data:
+            sock.close()
+            break
+
+        events = conn.receive_data(data)
+        for event in events:
+            if isinstance(event, h2.events.RequestReceived):
+                threading.Thread(target=send_response, args=(sock, conn, event)).start()
+
+
+class HTTP2Server:
+    def __init__(
+        self, *, host: str = "127.0.0.1", port: int = 0, timeout: float = 0.2
+    ) -> None:
+        self.sock = socket.socket()
+        self.sock.setsockopt(socket.SOL_SOCKET, socket.SO_REUSEADDR, 1)
+        self.sock.settimeout(timeout)
+        self.sock.bind((host, port))
+        self.port = self.sock.getsockname()[1]
+        self.sock.listen(5)
+
+    def run(self) -> None:
+        while True:
+            try:
+                handle(self.sock.accept()[0])
+            except socket.timeout:  # pragma: no cover
+                pass
+            except OSError:
+                break
+
+
+@contextlib.contextmanager
+def run(**kwargs):
+    server = HTTP2Server(**kwargs)
+    thr = threading.Thread(target=server.run)
+    thr.start()
+    try:
+        yield server
+    finally:
+        server.sock.close()
+        thr.join()
+
+
+if __name__ == "__main__":  # pragma: no cover
+    logging.basicConfig(
+        format="%(relativeCreated)5i <%(threadName)s> %(filename)s:%(lineno)s] %(message)s",
+        level=logging.INFO,
+    )
+
+    HTTP2Server(port=8100).run()