diff --git a/tests/async_tests/test_interfaces.py b/tests/async_tests/test_interfaces.py
index ac2483254..a00484ddc 100644
--- a/tests/async_tests/test_interfaces.py
+++ b/tests/async_tests/test_interfaces.py
@@ -1,5 +1,4 @@
 import platform
-import sys
 
 import pytest
 
@@ -469,39 +468,13 @@ 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 (this test is local-only)",
-)
 @pytest.mark.anyio
-async def test_connection_timeout_tcp(backend: str, server: Server) -> None:
-    # we try to access http server using https. It caused some SSL timeouts
-    # in TLSStream.wrap inside inside AnyIOBackend.open_tcp_stream
+async def test_connection_timeout_tcp(backend: str, busy_server: Server) -> None:
     method = b"GET"
-    url = (b"https", *server.netloc, b"/")
-    headers = [server.host_header]
-    ext = {"timeout": {"connect": 0.1}}
-
-    async with httpcore.AsyncConnectionPool(backend=backend) as http:
-        with pytest.raises(httpcore.ConnectTimeout):
-            await http.arequest(method, url, headers, ext=ext)
-
-
-@pytest.mark.skipif(
-    sys.version_info[:2] < (3, 7),
-    reason="Hypercorn doesn't support python < 3.7 (this test is local-only)",
-)
-@pytest.mark.anyio
-async def test_connection_timeout_uds(
-    backend: str, uds_server: Server, uds: str
-) -> None:
-    # we try to access http server using https. It caused some SSL timeouts
-    # in TLSStream.wrap inside AnyIOBackend.open_uds_stream
-    method = b"GET"
-    url = (b"https", b"localhost", None, b"/")
+    url = (b"http", *busy_server.netloc, b"/")
     headers = [(b"host", b"localhost")]
     ext = {"timeout": {"connect": 0.1}}
 
-    async with httpcore.AsyncConnectionPool(uds=uds, backend=backend) as http:
+    async with httpcore.AsyncConnectionPool(backend=backend) as http:
         with pytest.raises(httpcore.ConnectTimeout):
             await http.arequest(method, url, headers, ext=ext)
diff --git a/tests/conftest.py b/tests/conftest.py
index 0ba96fdc9..78e78f9be 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -9,7 +9,13 @@
 
 from httpcore._types import URL
 
-from .utils import HypercornServer, LiveServer, Server, http_proxy_server
+from .utils import (
+    HypercornServer,
+    LiveServer,
+    NotListeningServer,
+    Server,
+    http_proxy_server,
+)
 
 try:
     import hypercorn
@@ -25,6 +31,8 @@
     SERVER_HTTPS_PORT = 8003
     HTTPS_SERVER_URL = f"https://localhost:{SERVER_HTTPS_PORT}"
 
+SERVER_BUSY_PORT = 8004
+
 
 @pytest.fixture(scope="session")
 def proxy_server() -> typing.Iterator[URL]:
@@ -161,6 +169,13 @@ def https_server(
         yield server
 
 
+@pytest.fixture
+def busy_server() -> typing.Iterator[Server]:
+    server = NotListeningServer(("localhost", SERVER_BUSY_PORT))
+    with server.serve():
+        yield server
+
+
 @pytest.fixture(scope="function")
 def too_many_open_files_minus_one() -> typing.Iterator[None]:
     # Fixture for test regression on https://github.com/encode/httpcore/issues/182
diff --git a/tests/sync_tests/test_interfaces.py b/tests/sync_tests/test_interfaces.py
index e1db92c87..2d779cb2d 100644
--- a/tests/sync_tests/test_interfaces.py
+++ b/tests/sync_tests/test_interfaces.py
@@ -1,5 +1,4 @@
 import platform
-import sys
 
 import pytest
 
@@ -469,39 +468,13 @@ 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 (this test is local-only)",
-)
 
-def test_connection_timeout_tcp(backend: str, server: Server) -> None:
-    # we try to access http server using https. It caused some SSL timeouts
-    # in TLSStream.wrap inside inside AnyIOBackend.open_tcp_stream
+def test_connection_timeout_tcp(backend: str, busy_server: Server) -> None:
     method = b"GET"
-    url = (b"https", *server.netloc, b"/")
-    headers = [server.host_header]
-    ext = {"timeout": {"connect": 0.1}}
-
-    with httpcore.SyncConnectionPool(backend=backend) as http:
-        with pytest.raises(httpcore.ConnectTimeout):
-            http.request(method, url, headers, ext=ext)
-
-
-@pytest.mark.skipif(
-    sys.version_info[:2] < (3, 7),
-    reason="Hypercorn doesn't support python < 3.7 (this test is local-only)",
-)
-
-def test_connection_timeout_uds(
-    backend: str, uds_server: Server, uds: str
-) -> None:
-    # we try to access http server using https. It caused some SSL timeouts
-    # in TLSStream.wrap inside AnyIOBackend.open_uds_stream
-    method = b"GET"
-    url = (b"https", b"localhost", None, b"/")
+    url = (b"http", *busy_server.netloc, b"/")
     headers = [(b"host", b"localhost")]
     ext = {"timeout": {"connect": 0.1}}
 
-    with httpcore.SyncConnectionPool(uds=uds, backend=backend) as http:
+    with httpcore.SyncConnectionPool(backend=backend) as http:
         with pytest.raises(httpcore.ConnectTimeout):
             http.request(method, url, headers, ext=ext)
diff --git a/tests/utils.py b/tests/utils.py
index de3091255..05f7e4854 100644
--- a/tests/utils.py
+++ b/tests/utils.py
@@ -148,6 +148,27 @@ def serve_in_thread(self) -> Iterator[None]:
             thread.join()
 
 
+class NotListeningServer(Server):
+    """
+    A test server that binds to a TCP port but never listens for or accepts incoming
+    connections. For testing connection timeouts.
+    """
+
+    def __init__(self, address: Tuple[str, int]) -> None:
+        self._address = address
+
+    @property
+    def netloc(self) -> Tuple[bytes, int]:
+        host, port = self._address
+        return (host.encode("ascii"), port)
+
+    @contextlib.contextmanager
+    def serve(self) -> Iterator[None]:
+        with socket.socket(socket.AF_INET, socket.SOCK_STREAM) as sock:
+            sock.bind(self._address)
+            yield
+
+
 @contextlib.contextmanager
 def http_proxy_server(proxy_host: str, proxy_port: int):
     """