diff --git a/telethon/client/telegrambaseclient.py b/telethon/client/telegrambaseclient.py
index 43df209f..c79afdc0 100644
--- a/telethon/client/telegrambaseclient.py
+++ b/telethon/client/telegrambaseclient.py
@@ -308,7 +308,9 @@ class TelegramBaseClient(abc.ABC):
             self._updates_queue = asyncio.Queue(loop=self._loop)
             self._dispatching_updates_queue = asyncio.Event(loop=self._loop)
         else:
-            self._updates_queue = None
+            # Use a set of pending instead of a queue so we can properly
+            # terminate all pending updates on disconnect.
+            self._updates_queue = set()
             self._dispatching_updates_queue = None
 
         self._authorized = None  # None = unknown, False = no, True = yes
@@ -394,11 +396,28 @@ class TelegramBaseClient(abc.ABC):
         if self._loop.is_running():
             return self._disconnect_coro()
         else:
-            self._loop.run_until_complete(self._disconnect_coro())
+            try:
+                self._loop.run_until_complete(self._disconnect_coro())
+            except RuntimeError:
+                # Python 3.5.x complains when called from
+                # `__aexit__` and there were pending updates with:
+                #   "Event loop stopped before Future completed."
+                #
+                # However, it doesn't really make a lot of sense.
+                pass
 
     async def _disconnect_coro(self: 'TelegramClient'):
         await self._disconnect()
 
+        # trio's nurseries would handle this for us, but this is asyncio.
+        # All tasks spawned in the background should properly be terminated.
+        if self._dispatching_updates_queue is None and self._updates_queue:
+            for task in self._updates_queue:
+                task.cancel()
+
+            await asyncio.wait(self._updates_queue, loop=self._loop)
+            self._updates_queue.clear()
+
         pts, date = self._state_cache[None]
         self.session.set_update_state(0, types.updates.State(
             pts=pts,
diff --git a/telethon/client/updates.py b/telethon/client/updates.py
index a9d5c9aa..66eac4be 100644
--- a/telethon/client/updates.py
+++ b/telethon/client/updates.py
@@ -229,8 +229,10 @@ class UpdateMethods(UserMethods):
         # arguments which is faster.
         channel_id = self._state_cache.get_channel_id(update)
         args = (update, channel_id, self._state_cache[channel_id])
-        if self._updates_queue is None:
-            self._loop.create_task(self._dispatch_update(*args))
+        if self._dispatching_updates_queue is None:
+            task = self._loop.create_task(self._dispatch_update(*args))
+            self._updates_queue.add(task)
+            task.add_done_callback(lambda _: self._updates_queue.discard(task))
         else:
             self._updates_queue.put_nowait(args)
             if not self._dispatching_updates_queue.is_set():
@@ -343,10 +345,11 @@ class UpdateMethods(UserMethods):
                     'for event %s.', name, type(event).__name__
                 )
                 break
-            except Exception:
-                name = getattr(callback, '__name__', repr(callback))
-                self._log[__name__].exception('Unhandled exception on %s',
-                                              name)
+            except Exception as e:
+                if not isinstance(e, asyncio.CancelledError) or self.is_connected():
+                    name = getattr(callback, '__name__', repr(callback))
+                    self._log[__name__].exception('Unhandled exception on %s',
+                                                  name)
 
     async def _get_difference(self: 'TelegramClient', update, channel_id, pts_date):
         """