diff --git a/ansible_mitogen/process.py b/ansible_mitogen/process.py
index 4d3a9b5e..2b29904e 100644
--- a/ansible_mitogen/process.py
+++ b/ansible_mitogen/process.py
@@ -544,23 +544,12 @@ class ClassicWorkerModel(WorkerModel):
         """
         Used to clean up in unit tests.
         """
-        # TODO: split this up a bit.
-        global _classic_worker_model
-        assert self.parent_sock is not None
-        self.parent_sock.close()
-        self.parent_sock = None
-        self.listener_path = None
-        self.router = None
-        self.parent = None
-
-        for mux in self._muxes:
-            pid, status = os.waitpid(mux.pid, 0)
-            status = mitogen.fork._convert_exit_status(status)
-            LOG.debug('mux PID %d %s', pid,
-                mitogen.parent.returncode_to_str(status))
+        self.on_binding_close()
+        self._on_process_exit()
+        set_worker_model(None)
 
+        global _classic_worker_model
         _classic_worker_model = None
-        set_worker_model(None)
 
     def on_strategy_start(self):
         """
@@ -593,6 +582,7 @@ class ClassicWorkerModel(WorkerModel):
         self.broker.join()
         self.router = None
         self.broker = None
+        self.parent = None
         self.listener_path = None
 
         # #420: Ansible executes "meta" actions in the top-level process,
@@ -708,8 +698,8 @@ class MuxProcess(object):
             max_message_size=4096 * 1048576,
         )
         _setup_responder(self.router.responder)
-        mitogen.core.listen(self.broker, 'shutdown', self.on_broker_shutdown)
-        mitogen.core.listen(self.broker, 'exit', self.on_broker_exit)
+        mitogen.core.listen(self.broker, 'shutdown', self._on_broker_shutdown)
+        mitogen.core.listen(self.broker, 'exit', self._on_broker_exit)
         self.listener = mitogen.unix.Listener.build_stream(
             router=self.router,
             path=self.path,
@@ -729,26 +719,20 @@ class MuxProcess(object):
         )
         setup_pool(self.pool)
 
-    def on_broker_shutdown(self):
+    def _on_broker_shutdown(self):
         """
-        Respond to broker shutdown by beginning service pool shutdown. Do not
-        join on the pool yet, since that would block the broker thread which
-        then cannot clean up pending handlers, which is required for the
-        threads to exit gracefully.
+        Respond to broker shutdown by shutting down the pool. Do not join on it
+        yet, since that would block the broker thread which then cannot clean
+        up pending handlers and connections, which is required for the threads
+        to exit gracefully.
         """
-        # In normal operation we presently kill the process because there is
-        # not yet any way to cancel connect().
-        self.pool.stop(join=self.profiling)
+        self.pool.stop(join=False)
 
-    def on_broker_exit(self):
+    def _on_broker_exit(self):
         """
-        Respond to the broker thread about to exit by sending SIGTERM to
-        ourself. In future this should gracefully join the pool, but TERM is
-        fine for now.
+        Respond to the broker thread about to exit by finally joining on the
+        pool. This is safe since pools only block in connection attempts, and
+        connection attempts fail with CancelledError when broker shutdown
+        begins.
         """
-        if not os.environ.get('MITOGEN_PROFILING'):
-            # In normal operation we presently kill the process because there is
-            # not yet any way to cancel connect(). When profiling, threads
-            # including the broker must shut down gracefully, otherwise pstats
-            # won't be written.
-            os.kill(os.getpid(), signal.SIGTERM)
+        self.pool.join()