diff --git a/httpx/concurrency/asyncio.py b/httpx/concurrency/asyncio.py
index bb795b1d62..633801f73a 100644
--- a/httpx/concurrency/asyncio.py
+++ b/httpx/concurrency/asyncio.py
@@ -1,7 +1,6 @@
 import asyncio
 import functools
 import ssl
-import sys
 import typing
 
 from ..config import Timeout
@@ -162,9 +161,14 @@ def is_connection_dropped(self) -> bool:
         return self.stream_reader.at_eof()
 
     async def close(self) -> None:
+        # NOTE: StreamWriter instances expose a '.wait_closed()' coroutine function,
+        # but using it has caused compatibility issues with certain sites in
+        # the past (see https://github.com/encode/httpx/issues/634), which is
+        # why we don't call it here.
+        # This is fine, though, because '.close()' schedules the actual closing of the
+        # stream, meaning that at best it will happen during the next event loop
+        # iteration, and at worst asyncio will take care of it on program exit.
         self.stream_writer.close()
-        if sys.version_info >= (3, 7):
-            await self.stream_writer.wait_closed()
 
 
 class PoolSemaphore(BasePoolSemaphore):