diff --git a/tests/unit/http_clients/test_http_clients.py b/tests/unit/http_clients/test_http_clients.py
index d7e5541684..53eed5a145 100644
--- a/tests/unit/http_clients/test_http_clients.py
+++ b/tests/unit/http_clients/test_http_clients.py
@@ -413,14 +413,20 @@ async def test_read_twice_returns_same_body(http_client: HttpClient, server_url:
         assert await response.read() == HELLO_WORLD
 
 
-async def test_read_again_after_timeout(http_client: HttpClient, server_url: URL) -> None:
+async def test_read_again_after_timeout(
+    http_client: HttpClient, server_url: URL, monkeypatch: pytest.MonkeyPatch
+) -> None:
     """Test that a body read within the timeout is returned again by `read` once the timeout has passed."""
-    async with await http_client.send_request(str(server_url), timeout=timedelta(milliseconds=200)) as response:
-        body = await response.read()
+    loop = asyncio.get_running_loop()
+    loop_time = loop.time
 
-        await asyncio.sleep(0.3)
+    async with await http_client.send_request(str(server_url), timeout=timedelta(seconds=10)) as response:
+        body = await response.read()
 
-        assert await response.read() == body
+        # The response deadline is measured on the loop clock, so moving the clock passes it without waiting.
+        with monkeypatch.context() as m:
+            m.setattr(loop, 'time', lambda: loop_time() + 60)
+            assert await response.read() == body
 
 
 async def test_aclose_is_idempotent(http_client: HttpClient, server_url: URL) -> None:
@@ -891,7 +897,9 @@ async def handle(reader: asyncio.StreamReader, writer: asyncio.StreamWriter) ->
         async with response:
             assert await response.read() == b'ok'
 
-    connection_opened.assert_called_once()
+    # `impit` returns a drained connection to its pool in the background, so a request sent right after a close can
+    # still open a second connection. Dropping the connections of the closed responses would take three.
+    assert connection_opened.call_count <= 2
 
 
 @pytest.mark.parametrize(