diff --git a/Lib/asyncio/proactor_events.py b/Lib/asyncio/proactor_events.py
index ed17062..0f533a5 100644
--- a/Lib/asyncio/proactor_events.py
+++ b/Lib/asyncio/proactor_events.py
@@ -38,7 +38,7 @@
             self._server._attach()
         self._loop.call_soon(self._protocol.connection_made, self)
         if waiter is not None:
-            # wait until protocol.connection_made() has been called
+            # only wake up the waiter when connection_made() has been called
             self._loop.call_soon(waiter._set_result_unless_cancelled, None)
 
     def __repr__(self):
diff --git a/Lib/asyncio/selector_events.py b/Lib/asyncio/selector_events.py
index 24f8461..42d88f5 100644
--- a/Lib/asyncio/selector_events.py
+++ b/Lib/asyncio/selector_events.py
@@ -581,7 +581,7 @@
         self._loop.add_reader(self._sock_fd, self._read_ready)
         self._loop.call_soon(self._protocol.connection_made, self)
         if waiter is not None:
-            # wait until protocol.connection_made() has been called
+            # only wake up the waiter when connection_made() has been called
             self._loop.call_soon(waiter._set_result_unless_cancelled, None)
 
     def pause_reading(self):
@@ -732,6 +732,16 @@
             start_time = None
         self._on_handshake(start_time)
 
+    def _wakeup_waiter(self, exc=None):
+        if self._waiter is None:
+            return
+        if not self._waiter.cancelled():
+            if exc is not None:
+                self._waiter.set_exception(exc)
+            else:
+                self._waiter.set_result(None)
+        self._waiter = None
+
     def _on_handshake(self, start_time):
         try:
             self._sock.do_handshake()
@@ -750,8 +760,7 @@
             self._loop.remove_reader(self._sock_fd)
             self._loop.remove_writer(self._sock_fd)
             self._sock.close()
-            if self._waiter is not None and not self._waiter.cancelled():
-                self._waiter.set_exception(exc)
+            self._wakeup_waiter(exc)
             if isinstance(exc, Exception):
                 return
             else:
@@ -774,9 +783,7 @@
                                        "on matching the hostname",
                                        self, exc_info=True)
                     self._sock.close()
-                    if (self._waiter is not None
-                    and not self._waiter.cancelled()):
-                        self._waiter.set_exception(exc)
+                    self._wakeup_waiter(exc)
                     return
 
         # Add extra info that becomes available after handshake.
@@ -789,10 +796,8 @@
         self._write_wants_read = False
         self._loop.add_reader(self._sock_fd, self._read_ready)
         self._loop.call_soon(self._protocol.connection_made, self)
-        if self._waiter is not None:
-            # wait until protocol.connection_made() has been called
-            self._loop.call_soon(self._waiter._set_result_unless_cancelled,
-                                 None)
+        # only wake up the waiter when connection_made() has been called
+        self._loop.call_soon(self._wakeup_waiter)
 
         if self._loop.get_debug():
             dt = self._loop.time() - start_time
@@ -924,7 +929,7 @@
         self._loop.add_reader(self._sock_fd, self._read_ready)
         self._loop.call_soon(self._protocol.connection_made, self)
         if waiter is not None:
-            # wait until protocol.connection_made() has been called
+            # only wake up the waiter when connection_made() has been called
             self._loop.call_soon(waiter._set_result_unless_cancelled, None)
 
     def get_write_buffer_size(self):
diff --git a/Lib/asyncio/sslproto.py b/Lib/asyncio/sslproto.py
index 26937c8..fc809b9 100644
--- a/Lib/asyncio/sslproto.py
+++ b/Lib/asyncio/sslproto.py
@@ -418,6 +418,16 @@
         self._in_shutdown = False
         self._transport = None
 
+    def _wakeup_waiter(self, exc=None):
+        if self._waiter is None:
+            return
+        if not self._waiter.cancelled():
+            if exc is not None:
+                self._waiter.set_exception(exc)
+            else:
+                self._waiter.set_result(None)
+        self._waiter = None
+
     def connection_made(self, transport):
         """Called when the low-level connection is made.
 
@@ -490,8 +500,7 @@
             if self._loop.get_debug():
                 logger.debug("%r received EOF", self)
 
-            if self._waiter is not None and not self._waiter.done():
-                self._waiter.set_exception(ConnectionResetError())
+            self._wakeup_waiter(ConnectionResetError)
 
             if not self._in_handshake:
                 keep_open = self._app_protocol.eof_received()
@@ -556,8 +565,7 @@
                                    self, exc_info=True)
             self._transport.close()
             if isinstance(exc, Exception):
-                if self._waiter is not None and not self._waiter.cancelled():
-                    self._waiter.set_exception(exc)
+                self._wakeup_waiter(exc)
                 return
             else:
                 raise
@@ -572,9 +580,7 @@
                            compression=sslobj.compression(),
                            )
         self._app_protocol.connection_made(self._app_transport)
-        if self._waiter is not None:
-            # wait until protocol.connection_made() has been called
-            self._waiter._set_result_unless_cancelled(None)
+        self._wakeup_waiter()
         self._session_established = True
         # In case transport.write() was already called. Don't call
         # immediatly _process_write_backlog(), but schedule it:
diff --git a/Lib/asyncio/unix_events.py b/Lib/asyncio/unix_events.py
index 97f9add..67973f1 100644
--- a/Lib/asyncio/unix_events.py
+++ b/Lib/asyncio/unix_events.py
@@ -301,7 +301,7 @@
         self._loop.add_reader(self._fileno, self._read_ready)
         self._loop.call_soon(self._protocol.connection_made, self)
         if waiter is not None:
-            # wait until protocol.connection_made() has been called
+            # only wake up the waiter when connection_made() has been called
             self._loop.call_soon(waiter._set_result_unless_cancelled, None)
 
     def __repr__(self):
@@ -409,7 +409,7 @@
 
         self._loop.call_soon(self._protocol.connection_made, self)
         if waiter is not None:
-            # wait until protocol.connection_made() has been called
+            # only wake up the waiter when connection_made() has been called
             self._loop.call_soon(waiter._set_result_unless_cancelled, None)
 
     def __repr__(self):