diff --git a/tests/kafkatest/tests/connect/connect_distributed_test.py b/tests/kafkatest/tests/connect/connect_distributed_test.py
index 244bc64836ff6..107c0d4290597 100644
--- a/tests/kafkatest/tests/connect/connect_distributed_test.py
+++ b/tests/kafkatest/tests/connect/connect_distributed_test.py
@@ -387,8 +387,22 @@ def test_bounce(self, clean, connect_protocol):
                 # through the test.
                 time.sleep(15)
 
+        # Wait at least scheduled.rebalance.max.delay.ms to expire and rebalance
+        time.sleep(60)
 
+        # Allow the connectors to startup, recover, and exit cleanly before
+        # ending the test. It's possible for the source connector to make
+        # uncommitted progress, and for the sink connector to read messages that
+        # have not been committed yet, and fail a later assertion.
+        wait_until(lambda: self.is_running(self.source), timeout_sec=30,
+                   err_msg="Failed to see connector transition to the RUNNING state")
+        time.sleep(15)
         self.source.stop()
+        # Ensure that the sink connector has an opportunity to read all
+        # committed messages from the source connector.
+        wait_until(lambda: self.is_running(self.sink), timeout_sec=30,
+                   err_msg="Failed to see connector transition to the RUNNING state")
+        time.sleep(15)
         self.sink.stop()
         self.cc.stop()