diff --git a/Lib/asyncio/streams.py b/Lib/asyncio/streams.py
index 50badd6b247..d6531f88a74 100644
--- a/Lib/asyncio/streams.py
+++ b/Lib/asyncio/streams.py
@@ -208,9 +208,6 @@ class FlowControlMixin(protocols.Protocol):
         self._drain_waiter = waiter
         await waiter
 
-    def _get_close_waiter(self, stream):
-        raise NotImplementedError
-
 
 class StreamReaderProtocol(FlowControlMixin, protocols.Protocol):
     """Helper class to adapt between Protocol and StreamReader.
@@ -268,9 +265,6 @@ class StreamReaderProtocol(FlowControlMixin, protocols.Protocol):
             return False
         return True
 
-    def _get_close_waiter(self, stream):
-        return self._closed
-
     def __del__(self):
         # Prevent reports about unhandled exceptions.
         # Better than self._closed._log_traceback = False hack
@@ -326,7 +320,7 @@ class StreamWriter:
         return self._transport.is_closing()
 
     async def wait_closed(self):
-        await self._protocol._get_close_waiter(self)
+        await self._protocol._closed
 
     def get_extra_info(self, name, default=None):
         return self._transport.get_extra_info(name, default)
@@ -344,12 +338,13 @@ class StreamWriter:
             if exc is not None:
                 raise exc
         if self._transport.is_closing():
-            # Wait for protocol.connection_lost() call
-            # Raise connection closing error if any,
-            # ConnectionResetError otherwise
-            fut = self._protocol._get_close_waiter(self)
-            await fut
-            raise ConnectionResetError('Connection lost')
+            # Yield to the event loop so connection_lost() may be
+            # called.  Without this, _drain_helper() would return
+            # immediately, and code that calls
+            #     write(...); await drain()
+            # in a loop would never call connection_lost(), so it
+            # would not see an error when the socket is closed.
+            await sleep(0, loop=self._loop)
         await self._protocol._drain_helper()
 
 
diff --git a/Lib/asyncio/subprocess.py b/Lib/asyncio/subprocess.py
index ecacc1a66db..90fc00de833 100644
--- a/Lib/asyncio/subprocess.py
+++ b/Lib/asyncio/subprocess.py
@@ -25,7 +25,6 @@ class SubprocessStreamProtocol(streams.FlowControlMixin,
         self._transport = None
         self._process_exited = False
         self._pipe_fds = []
-        self._stdin_closed = self._loop.create_future()
 
     def __repr__(self):
         info = [self.__class__.__name__]
@@ -77,10 +76,6 @@ class SubprocessStreamProtocol(streams.FlowControlMixin,
             if pipe is not None:
                 pipe.close()
             self.connection_lost(exc)
-            if exc is None:
-                self._stdin_closed.set_result(None)
-            else:
-                self._stdin_closed.set_exception(exc)
             return
         if fd == 1:
             reader = self.stdout
@@ -107,10 +102,6 @@ class SubprocessStreamProtocol(streams.FlowControlMixin,
             self._transport.close()
             self._transport = None
 
-    def _get_close_waiter(self, stream):
-        if stream is self.stdin:
-            return self._stdin_closed
-
 
 class Process:
     def __init__(self, transport, protocol, loop):
diff --git a/Lib/test/test_asyncio/test_streams.py b/Lib/test/test_asyncio/test_streams.py
index 2e5fc61bce2..63fa13f79e2 100644
--- a/Lib/test/test_asyncio/test_streams.py
+++ b/Lib/test/test_asyncio/test_streams.py
@@ -99,29 +99,6 @@ class StreamTests(test_utils.TestCase):
 
             self._basetest_open_connection_no_loop_ssl(conn_fut)
 
-    @unittest.skipIf(ssl is None, 'No ssl module')
-    def test_drain_on_closed_writer_ssl(self):
-
-        async def inner(httpd):
-            reader, writer = await asyncio.open_connection(
-                *httpd.address,
-                ssl=test_utils.dummy_ssl_context())
-
-            messages = []
-            self.loop.set_exception_handler(lambda loop, ctx: messages.append(ctx))
-            writer.write(b'GET / HTTP/1.0\r\n\r\n')
-            data = await reader.read()
-            self.assertTrue(data.endswith(b'\r\n\r\nTest message'))
-
-            writer.close()
-            with self.assertRaises(ConnectionResetError):
-                await writer.drain()
-
-            self.assertEqual(messages, [])
-
-        with test_utils.run_test_server(use_ssl=True) as httpd:
-            self.loop.run_until_complete(inner(httpd))
-
     def _basetest_open_connection_error(self, open_connection_fut):
         reader, writer = self.loop.run_until_complete(open_connection_fut)
         writer._protocol.connection_lost(ZeroDivisionError())
diff --git a/Misc/NEWS.d/next/Library/2019-05-05-09-45-44.bpo-36801.XrlFFs.rst b/Misc/NEWS.d/next/Library/2019-05-05-09-45-44.bpo-36801.XrlFFs.rst
deleted file mode 100644
index 43e51fe5ca9..00000000000
--- a/Misc/NEWS.d/next/Library/2019-05-05-09-45-44.bpo-36801.XrlFFs.rst
+++ /dev/null
@@ -1 +0,0 @@
-Properly handle SSL connection closing in asyncio StreamWriter.drain() call.