diff --git a/Lib/asyncio/locks.py b/Lib/asyncio/locks.py
index 6193837..508a214 100644
--- a/Lib/asyncio/locks.py
+++ b/Lib/asyncio/locks.py
@@ -183,16 +183,22 @@
 
         fut = self._loop.create_future()
         self._waiters.append(fut)
+
+        # Finally block should be called before the CancelledError
+        # handling as we don't want CancelledError to call
+        # _wake_up_first() and attempt to wake up itself.
         try:
-            await fut
-            self._locked = True
-            return True
+            try:
+                await fut
+            finally:
+                self._waiters.remove(fut)
         except futures.CancelledError:
             if not self._locked:
                 self._wake_up_first()
             raise
-        finally:
-            self._waiters.remove(fut)
+
+        self._locked = True
+        return True
 
     def release(self):
         """Release a lock.
@@ -212,11 +218,17 @@
             raise RuntimeError('Lock is not acquired.')
 
     def _wake_up_first(self):
-        """Wake up the first waiter who isn't cancelled."""
-        for fut in self._waiters:
-            if not fut.done():
-                fut.set_result(True)
-                break
+        """Wake up the first waiter if it isn't done."""
+        try:
+            fut = next(iter(self._waiters))
+        except StopIteration:
+            return
+
+        # .done() necessarily means that a waiter will wake up later on and
+        # either take the lock, or, if it was cancelled and lock wasn't
+        # taken already, will hit this again and wake up a new waiter.
+        if not fut.done():
+            fut.set_result(True)
 
 
 class Event: