diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 74d402ff..31197209 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -10,6 +10,10 @@ and this project adheres to `Semantic Versioning <https://semver.org/spec/v2.0.0
 `Unreleased`_
 =============
 
+Fixed
+-----
+* Fixed ``TimeoutError`` when connecting to certain devices with WinRT backend. Fixes #604.
+
 `0.19.2`_ (2022-11-06)
 ======================
 
diff --git a/bleak/backends/winrt/client.py b/bleak/backends/winrt/client.py
index 64659804..5121756b 100644
--- a/bleak/backends/winrt/client.py
+++ b/bleak/backends/winrt/client.py
@@ -366,18 +366,30 @@ def max_pdu_size_changed_handler(sender: GattSession, args):
             self._session.maintain_connection = True
             # This keeps the device connected until we set maintain_connection = False.
 
-            # wait for the session to become active
-            async with async_timeout.timeout(timeout):
-                await event.wait()
+            wait_connect_task = asyncio.create_task(event.wait())
+
+            try:
+                # a connection may not be made until we request info from the
+                # device, so we have to get services before the GATT session
+                # is set to active
+                wait_get_services_task = asyncio.create_task(self.get_services())
+
+                try:
+                    # wait for the session to become active
+                    async with async_timeout(timeout):
+                        await asyncio.gather(wait_connect_task, wait_get_services_task)
+
+                finally:
+                    wait_get_services_task.cancel()
+            finally:
+                wait_connect_task.cancel()
+
         except BaseException:
             handle_disconnect()
             raise
         finally:
             self._session_active_events.remove(event)
 
-        # Obtain services, which also leads to connection being established.
-        await self.get_services()
-
         return True
 
     async def disconnect(self) -> bool:
@@ -540,8 +552,6 @@ async def get_services(self, **kwargs) -> BleakGATTServiceCollection:
            A :py:class:`bleak.backends.service.BleakGATTServiceCollection` with this device's services tree.
 
         """
-        if not self.is_connected:
-            raise BleakError("Not connected")
 
         # Return the Service Collection.
         if self._services_resolved: