diff --git a/pubsub/google/cloud/pubsub_v1/subscriber/_protocol/streaming_pull_manager.py b/pubsub/google/cloud/pubsub_v1/subscriber/_protocol/streaming_pull_manager.py
index b393cbfd5ec6..c4f64a1aa8c5 100644
--- a/pubsub/google/cloud/pubsub_v1/subscriber/_protocol/streaming_pull_manager.py
+++ b/pubsub/google/cloud/pubsub_v1/subscriber/_protocol/streaming_pull_manager.py
@@ -44,6 +44,7 @@
     exceptions.GatewayTimeout,
     exceptions.Aborted,
 )
+_TERMINATING_STREAM_ERRORS = (exceptions.Cancelled,)
 _MAX_LOAD = 1.0
 """The load threshold above which to pause the incoming message stream."""
 
@@ -394,6 +395,7 @@ def open(self, callback, on_callback_error):
             start_rpc=self._client.api.streaming_pull,
             initial_request=get_initial_request,
             should_recover=self._should_recover,
+            should_terminate=self._should_terminate,
             throttle_reopen=True,
         )
         self._rpc.add_done_callback(self._on_rpc_done)
@@ -582,6 +584,26 @@ def _should_recover(self, exception):
         _LOGGER.info("Observed non-recoverable stream error %s", exception)
         return False
 
+    def _should_terminate(self, exception):
+        """Determine if an error on the RPC stream should be terminated.
+
+        If the exception is one of the terminating exceptions, this will signal
+        to the consumer thread that it should terminate.
+
+        This will cause the stream to exit when it returns :data:`True`.
+
+        Returns:
+            bool: Indicates if the caller should terminate or attempt recovery.
+            Will be :data:`True` if the ``exception`` is "acceptable", i.e.
+            in a list of terminating exceptions.
+        """
+        exception = _maybe_wrap_exception(exception)
+        if isinstance(exception, _TERMINATING_STREAM_ERRORS):
+            _LOGGER.info("Observed terminating stream error %s", exception)
+            return True
+        _LOGGER.info("Observed non-terminating stream error %s", exception)
+        return False
+
     def _on_rpc_done(self, future):
         """Triggered whenever the underlying RPC terminates without recovery.
 
diff --git a/pubsub/tests/unit/pubsub_v1/subscriber/test_streaming_pull_manager.py b/pubsub/tests/unit/pubsub_v1/subscriber/test_streaming_pull_manager.py
index 352b09ba83fc..1b72f48dc9f6 100644
--- a/pubsub/tests/unit/pubsub_v1/subscriber/test_streaming_pull_manager.py
+++ b/pubsub/tests/unit/pubsub_v1/subscriber/test_streaming_pull_manager.py
@@ -433,6 +433,7 @@ def test_open(heartbeater, dispatcher, leaser, background_consumer, resumable_bi
         start_rpc=manager._client.api.streaming_pull,
         initial_request=mock.ANY,
         should_recover=manager._should_recover,
+        should_terminate=manager._should_terminate,
         throttle_reopen=True,
     )
     initial_request_arg = resumable_bidi_rpc.call_args.kwargs["initial_request"]
@@ -726,6 +727,23 @@ def test__should_recover_false():
     assert manager._should_recover(exc) is False
 
 
+def test__should_terminate_true():
+    manager = make_manager()
+
+    details = "Cancelled. Go away, before I taunt you a second time."
+    exc = exceptions.Cancelled(details)
+
+    assert manager._should_terminate(exc) is True
+
+
+def test__should_terminate_false():
+    manager = make_manager()
+
+    exc = TypeError("wahhhhhh")
+
+    assert manager._should_terminate(exc) is False
+
+
 @mock.patch("threading.Thread", autospec=True)
 def test__on_rpc_done(thread):
     manager = make_manager()