diff --git a/tests/async_tests/test_interfaces.py b/tests/async_tests/test_interfaces.py
index f21842e6f..136915559 100644
--- a/tests/async_tests/test_interfaces.py
+++ b/tests/async_tests/test_interfaces.py
@@ -469,6 +469,9 @@ async def test_cannot_connect_uds(backend: str) -> None:
             await http.arequest(method, url)
 
 
+@pytest.mark.skipif(
+    sys.version_info[:2] < (3, 7), reason="Hypercorn doesn't support python < 3.7"
+)
 @pytest.mark.anyio
 async def test_connection_timeout_tcp(backend: str, slow_tcp_server: Server) -> None:
     method = b"GET"
diff --git a/tests/conftest.py b/tests/conftest.py
index 3e7813353..40c4870e0 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -20,15 +20,14 @@
     SERVER_HTTP_PORT = 80
     SERVER_HTTPS_PORT = 443
     HTTPS_SERVER_URL = "https://example.org"
-    SLOW_SERVER_HOST = "httpbin.org"
-    SLOW_SERVER_PORT = 443
 else:
     SERVER_HOST = "localhost"
     SERVER_HTTP_PORT = 8002
     SERVER_HTTPS_PORT = 8003
     HTTPS_SERVER_URL = f"https://localhost:{SERVER_HTTPS_PORT}"
-    SLOW_SERVER_HOST = SERVER_HOST
-    SLOW_SERVER_PORT = 8004
+
+SLOW_SERVER_HOST = SERVER_HOST
+SLOW_SERVER_PORT = 8004
 
 
 @pytest.fixture(scope="session")
@@ -194,18 +193,14 @@ def https_server(
 
 @pytest.fixture(scope="session")
 def slow_tcp_server() -> typing.Iterator[Server]:
-    server: Server
+    assert hypercorn is not None
 
-    if hypercorn is None:
-        server = LiveServer(host=SLOW_SERVER_HOST, port=SLOW_SERVER_PORT)
-        yield server
-    else:
-        server = HypercornServer(
-            app=slow_app, bind=f"{SLOW_SERVER_HOST}:{SLOW_SERVER_PORT}"
-        )
+    server = HypercornServer(
+        app=slow_app, bind=f"{SLOW_SERVER_HOST}:{SLOW_SERVER_PORT}"
+    )
 
-        with server.serve_in_thread():
-            yield server
+    with server.serve_in_thread():
+        yield server
 
 
 @pytest.fixture(scope="function")
diff --git a/tests/sync_tests/test_interfaces.py b/tests/sync_tests/test_interfaces.py
index a78586488..ec0c1213a 100644
--- a/tests/sync_tests/test_interfaces.py
+++ b/tests/sync_tests/test_interfaces.py
@@ -469,6 +469,9 @@ def test_cannot_connect_uds(backend: str) -> None:
             http.request(method, url)
 
 
+@pytest.mark.skipif(
+    sys.version_info[:2] < (3, 7), reason="Hypercorn doesn't support python < 3.7"
+)
 
 def test_connection_timeout_tcp(backend: str, slow_tcp_server: Server) -> None:
     method = b"GET"