diff --git a/tests/test_asyncio/test_connection.py b/tests/test_asyncio/test_connection.py
index 3a611206b7..6d6b3b9d2c 100644
--- a/tests/test_asyncio/test_connection.py
+++ b/tests/test_asyncio/test_connection.py
@@ -1,7 +1,7 @@
 import asyncio
 import socket
 import types
-from unittest.mock import AsyncMock, Mock, patch
+from unittest.mock import patch
 
 import pytest
 
@@ -151,7 +151,10 @@ async def test_connection_parse_response_resume(r: redis.Redis):
 
 
 @pytest.mark.onlynoncluster
-async def test_connection_hiredis_disconect_race():
+@pytest.mark.parametrize(
+    "parser_class", [PythonParser, HiredisParser], ids=["PythonParser", "HiredisParser"]
+)
+async def test_connection_disconect_race(parser_class):
     """
     This test reproduces the case in issue #2349
     where a connection is closed while the parser is reading to feed the
@@ -163,12 +166,14 @@ async def test_connection_hiredis_disconect_race():
     This test verifies that a read in progress can finish even
     if the `disconnect()` method is called.
     """
-    if not HIREDIS_AVAILABLE:
-        pytest.skip("Hiredis not available)")
-    parser_class = HiredisParser
+    if parser_class == PythonParser:
+        pytest.xfail("doesn't work yet with PythonParser")
+    if parser_class == HiredisParser and not HIREDIS_AVAILABLE:
+        pytest.skip("Hiredis not available")
 
     args = {}
     args["parser_class"] = parser_class
+
     conn = Connection(**args)
 
     cond = asyncio.Condition()
@@ -177,15 +182,20 @@ async def test_connection_hiredis_disconect_race():
     # 2 == closer has closed and is waiting for close to finish
     state = 0
 
-    # mock read function, which wait for a close to happen before returning
-    async def read(_):
+    # Mock read function, which wait for a close to happen before returning
+    # Can either be invoked as two `read()` calls (HiredisParser)
+    # or as a `readline()` followed by `readexact()` (PythonParser)
+    chunks = [b"$13\r\n", b"Hello, World!\r\n"]
+
+    async def read(_=None):
         nonlocal state
         async with cond:
-            state = 1  # we are reading
-            cond.notify()
-            # wait until the closing task has done
-            await cond.wait_for(lambda: state == 2)
-        return b" "
+            if state == 0:
+                state = 1  # we are reading
+                cond.notify()
+                # wait until the closing task has done
+                await cond.wait_for(lambda: state == 2)
+        return chunks.pop(0)
 
     # function closes the connection while reader is still blocked reading
     async def do_close():
@@ -197,15 +207,18 @@ async def do_close():
         await conn.disconnect()
 
     async def do_read():
-        with pytest.raises(InvalidResponse):
-            await conn.read_response()
+        return await conn.read_response()
 
-    reader = AsyncMock()
-    writer = AsyncMock()
-    writer.transport = Mock()
+    reader = mock.AsyncMock()
+    writer = mock.AsyncMock()
+    writer.transport = mock.Mock()
     writer.transport.get_extra_info.side_effect = None
 
+    # for HiredisParser
     reader.read.side_effect = read
+    # for PythonParser
+    reader.readline.side_effect = read
+    reader.readexactly.side_effect = read
 
     async def open_connection(*args, **kwargs):
         return reader, writer
@@ -213,4 +226,5 @@ async def open_connection(*args, **kwargs):
     with patch.object(asyncio, "open_connection", open_connection):
         await conn.connect()
 
-    await asyncio.gather(do_read(), do_close())
+    vals = await asyncio.gather(do_read(), do_close())
+    assert vals == [b"Hello, World!", None]