diff --git a/Lib/asyncio/selector_events.py b/Lib/asyncio/selector_events.py
index a05cbb6bdd..8850fd534b 100644
--- a/Lib/asyncio/selector_events.py
+++ b/Lib/asyncio/selector_events.py
@@ -266,6 +266,7 @@ class BaseSelectorEventLoop(base_events.BaseEventLoop):
                                   (handle, writer))
             if reader is not None:
                 reader.cancel()
+        return handle
 
     def _remove_reader(self, fd):
         if self.is_closed():
@@ -302,6 +303,7 @@ class BaseSelectorEventLoop(base_events.BaseEventLoop):
                                   (reader, handle))
             if writer is not None:
                 writer.cancel()
+        return handle
 
     def _remove_writer(self, fd):
         """Remove a writer callback."""
@@ -362,13 +364,14 @@ class BaseSelectorEventLoop(base_events.BaseEventLoop):
             pass
         fut = self.create_future()
         fd = sock.fileno()
-        self.add_reader(fd, self._sock_recv, fut, sock, n)
+        handle = self.add_reader(fd, self._sock_recv, fut, sock, n)
         fut.add_done_callback(
-            functools.partial(self._sock_read_done, fd))
+            functools.partial(self._sock_read_done, fd, handle))
         return await fut
 
-    def _sock_read_done(self, fd, fut):
-        self.remove_reader(fd)
+    def _sock_read_done(self, fd, handle, fut):
+        if not handle.cancelled():
+            self.remove_reader(fd)
 
     def _sock_recv(self, fut, sock, n):
         # _sock_recv() can add itself as an I/O callback if the operation can't
@@ -401,9 +404,9 @@ class BaseSelectorEventLoop(base_events.BaseEventLoop):
             pass
         fut = self.create_future()
         fd = sock.fileno()
-        self.add_reader(fd, self._sock_recv_into, fut, sock, buf)
+        handle = self.add_reader(fd, self._sock_recv_into, fut, sock, buf)
         fut.add_done_callback(
-            functools.partial(self._sock_read_done, fd))
+            functools.partial(self._sock_read_done, fd, handle))
         return await fut
 
     def _sock_recv_into(self, fut, sock, buf):