diff --git a/redis/asyncio/connection.py b/redis/asyncio/connection.py
index 8fbb0b17a0..a7a749d4a0 100644
--- a/redis/asyncio/connection.py
+++ b/redis/asyncio/connection.py
@@ -826,7 +826,7 @@ async def on_connect(self) -> None:
             if str_if_bytes(await self.read_response()) != "OK":
                 raise ConnectionError("Invalid Database")
 
-    async def disconnect(self) -> None:
+    async def disconnect(self, nowait: bool = False) -> None:
         """Disconnects from the Redis server"""
         try:
             async with async_timeout.timeout(self.socket_connect_timeout):
@@ -836,8 +836,9 @@ async def disconnect(self) -> None:
                 try:
                     if os.getpid() == self.pid:
                         self._writer.close()  # type: ignore[union-attr]
-                        # py3.6 doesn't have this method
-                        if hasattr(self._writer, "wait_closed"):
+                        # wait for close to finish, except when handling errors and
+                        # forcecully disconnecting.
+                        if not nowait:
                             await self._writer.wait_closed()  # type: ignore[union-attr]
                 except OSError:
                     pass
@@ -938,10 +939,10 @@ async def read_response(self, disable_decoding: bool = False):
                         disable_decoding=disable_decoding
                     )
         except asyncio.TimeoutError:
-            await self.disconnect()
+            await self.disconnect(nowait=True)
             raise TimeoutError(f"Timeout reading from {self.host}:{self.port}")
         except OSError as e:
-            await self.disconnect()
+            await self.disconnect(nowait=True)
             raise ConnectionError(
                 f"Error while reading from {self.host}:{self.port} : {e.args}"
             )
@@ -950,7 +951,7 @@ async def read_response(self, disable_decoding: bool = False):
             # is subclass of Exception, not BaseException
             raise
         except Exception:
-            await self.disconnect()
+            await self.disconnect(nowait=True)
             raise
 
         if self.health_check_interval: