diff --git a/test/asynchronous/test_client.py b/test/asynchronous/test_client.py
index 744a170be2..4758ce3dda 100644
--- a/test/asynchronous/test_client.py
+++ b/test/asynchronous/test_client.py
@@ -1824,20 +1824,20 @@ def server_description_count():
             return i
 
         gc.collect()
-        with client_knobs(min_heartbeat_interval=0.003):
+        with client_knobs(min_heartbeat_interval=0.002):
             client = self.simple_client(
-                "invalid:27017", heartbeatFrequencyMS=3, serverSelectionTimeoutMS=150
+                "invalid:27017", heartbeatFrequencyMS=2, serverSelectionTimeoutMS=200
             )
             initial_count = server_description_count()
             with self.assertRaises(ServerSelectionTimeoutError):
                 await client.test.test.find_one()
             gc.collect()
             final_count = server_description_count()
+            await client.close()
             # If a bug like PYTHON-2433 is reintroduced then too many
             # ServerDescriptions will be kept alive and this test will fail:
-            # AssertionError: 19 != 46 within 15 delta (27 difference)
-            # On Python 3.11 we seem to get more of a delta.
-            self.assertAlmostEqual(initial_count, final_count, delta=20)
+            # AssertionError: 11 != 47 within 20 delta (36 difference)
+            self.assertAlmostEqual(initial_count, final_count, delta=30)
 
     @async_client_context.require_failCommand_fail_point
     async def test_network_error_message(self):
diff --git a/test/test_client.py b/test/test_client.py
index cdc7691c28..aa321d2925 100644
--- a/test/test_client.py
+++ b/test/test_client.py
@@ -1781,20 +1781,20 @@ def server_description_count():
             return i
 
         gc.collect()
-        with client_knobs(min_heartbeat_interval=0.003):
+        with client_knobs(min_heartbeat_interval=0.002):
             client = self.simple_client(
-                "invalid:27017", heartbeatFrequencyMS=3, serverSelectionTimeoutMS=150
+                "invalid:27017", heartbeatFrequencyMS=2, serverSelectionTimeoutMS=200
             )
             initial_count = server_description_count()
             with self.assertRaises(ServerSelectionTimeoutError):
                 client.test.test.find_one()
             gc.collect()
             final_count = server_description_count()
+            client.close()
             # If a bug like PYTHON-2433 is reintroduced then too many
             # ServerDescriptions will be kept alive and this test will fail:
-            # AssertionError: 19 != 46 within 15 delta (27 difference)
-            # On Python 3.11 we seem to get more of a delta.
-            self.assertAlmostEqual(initial_count, final_count, delta=20)
+            # AssertionError: 11 != 47 within 20 delta (36 difference)
+            self.assertAlmostEqual(initial_count, final_count, delta=30)
 
     @client_context.require_failCommand_fail_point
     def test_network_error_message(self):