diff --git a/Lib/asyncio/proactor_events.py b/Lib/asyncio/proactor_events.py
index 8338449..6b6bf89 100644
--- a/Lib/asyncio/proactor_events.py
+++ b/Lib/asyncio/proactor_events.py
@@ -766,6 +766,14 @@
         try:
             if f is not None:
                 f.result()  # may raise
+            if self._self_reading_future is not f:
+                # When we scheduled this Future, we assigned it to
+                # _self_reading_future. If it's not there now, something has
+                # tried to cancel the loop while this callback was still in the
+                # queue (see windows_events.ProactorEventLoop.run_forever). In
+                # that case stop here instead of continuing to schedule a new
+                # iteration.
+                return
             f = self._proactor.recv(self._ssock, 4096)
         except exceptions.CancelledError:
             # _close_self_pipe() has been called, stop waiting for data
diff --git a/Lib/asyncio/windows_events.py b/Lib/asyncio/windows_events.py
index a6759b7..5e7cd79 100644
--- a/Lib/asyncio/windows_events.py
+++ b/Lib/asyncio/windows_events.py
@@ -318,8 +318,12 @@
             if self._self_reading_future is not None:
                 ov = self._self_reading_future._ov
                 self._self_reading_future.cancel()
-                # self_reading_future was just cancelled so it will never be signalled
-                # Unregister it otherwise IocpProactor.close will wait for it forever
+                # self_reading_future was just cancelled so if it hasn't been
+                # finished yet, it never will be (it's possible that it has
+                # already finished and its callback is waiting in the queue,
+                # where it could still happen if the event loop is restarted).
+                # Unregister it otherwise IocpProactor.close will wait for it
+                # forever
                 if ov is not None:
                     self._proactor._unregister(ov)
                 self._self_reading_future = None
diff --git a/Lib/test/test_asyncio/test_proactor_events.py b/Lib/test/test_asyncio/test_proactor_events.py
index b5d1df9..451f86a 100644
--- a/Lib/test/test_asyncio/test_proactor_events.py
+++ b/Lib/test/test_asyncio/test_proactor_events.py
@@ -737,6 +737,7 @@
 
     def test_loop_self_reading_fut(self):
         fut = mock.Mock()
+        self.loop._self_reading_future = fut
         self.loop._loop_self_reading(fut)
         self.assertTrue(fut.result.called)
         self.proactor.recv.assert_called_with(self.ssock, 4096)
diff --git a/Lib/test/test_asyncio/test_windows_events.py b/Lib/test/test_asyncio/test_windows_events.py
index 6b00570..33388a8 100644
--- a/Lib/test/test_asyncio/test_windows_events.py
+++ b/Lib/test/test_asyncio/test_windows_events.py
@@ -211,6 +211,26 @@
         fut.cancel()
         fut.cancel()
 
+    def test_read_self_pipe_restart(self):
+        # Regression test for https://bugs.python.org/issue39010
+        # Previously, restarting a proactor event loop in certain states
+        # would lead to spurious ConnectionResetErrors being logged.
+        self.loop.call_exception_handler = mock.Mock()
+        # Start an operation in another thread so that the self-pipe is used.
+        # This is theoretically timing-dependent (the task in the executor
+        # must complete before our start/stop cycles), but in practice it
+        # seems to work every time.
+        f = self.loop.run_in_executor(None, lambda: None)
+        self.loop.stop()
+        self.loop.run_forever()
+        self.loop.stop()
+        self.loop.run_forever()
+        # If we don't wait for f to complete here, we may get another
+        # warning logged about a thread that didn't shut down cleanly.
+        self.loop.run_until_complete(f)
+        self.loop.close()
+        self.assertFalse(self.loop.call_exception_handler.called)
+
 
 class WinPolicyTests(test_utils.TestCase):