diff --git a/test/test_client.py b/test/test_client.py
index 59a8324d6e..3630cec06c 100644
--- a/test/test_client.py
+++ b/test/test_client.py
@@ -1596,7 +1596,6 @@ def test_direct_connection(self):
         with self.assertRaises(ConfigurationError):
             MongoClient(["host1", "host2"], directConnection=True)
 
-    @unittest.skipIf(sys.platform.startswith("java"), "Jython does not support gc.get_objects")
     @unittest.skipIf("PyPy" in sys.version, "PYTHON-2927 fails often on PyPy")
     def test_continuous_network_errors(self):
         def server_description_count():
@@ -1612,7 +1611,7 @@ def server_description_count():
         gc.collect()
         with client_knobs(min_heartbeat_interval=0.003):
             client = MongoClient(
-                "invalid:27017", heartbeatFrequencyMS=3, serverSelectionTimeoutMS=100
+                "invalid:27017", heartbeatFrequencyMS=3, serverSelectionTimeoutMS=150
             )
             initial_count = server_description_count()
             self.addCleanup(client.close)
@@ -1622,8 +1621,8 @@ def server_description_count():
             final_count = server_description_count()
             # If a bug like PYTHON-2433 is reintroduced then too many
             # ServerDescriptions will be kept alive and this test will fail:
-            # AssertionError: 4 != 22 within 5 delta (18 difference)
-            self.assertAlmostEqual(initial_count, final_count, delta=10)
+            # AssertionError: 19 != 46 within 15 delta (27 difference)
+            self.assertAlmostEqual(initial_count, final_count, delta=15)
 
     @client_context.require_failCommand_fail_point
     def test_network_error_message(self):
diff --git a/test/test_transactions.py b/test/test_transactions.py
index 34dbbba34b..136a19baaa 100644
--- a/test/test_transactions.py
+++ b/test/test_transactions.py
@@ -30,6 +30,8 @@
 )
 from test.utils_spec_runner import SpecRunner
 
+from bson import encode
+from bson.raw_bson import RawBSONDocument
 from gridfs import GridFS, GridFSBucket
 from pymongo import WriteConcern, client_session
 from pymongo.client_session import TransactionOptions
@@ -330,14 +332,14 @@ def test_transaction_starts_with_batched_write(self):
         listener.reset()
         self.addCleanup(client.close)
         self.addCleanup(coll.drop)
-        large_str = "\0" * (10 * 1024 * 1024)
-        ops = [InsertOne({"a": large_str}) for _ in range(10)]
+        large_str = "\0" * (1 * 1024 * 1024)
+        ops = [InsertOne(RawBSONDocument(encode({"a": large_str}))) for _ in range(48)]
         with client.start_session() as session:
             with session.start_transaction():
                 coll.bulk_write(ops, session=session)
         # Assert commands were constructed properly.
         self.assertEqual(
-            ["insert", "insert", "insert", "commitTransaction"], listener.started_command_names()
+            ["insert", "insert", "commitTransaction"], listener.started_command_names()
         )
         first_cmd = listener.results["started"][0].command
         self.assertTrue(first_cmd["startTransaction"])
@@ -347,7 +349,7 @@ def test_transaction_starts_with_batched_write(self):
             self.assertNotIn("startTransaction", event.command)
             self.assertEqual(lsid, event.command["lsid"])
             self.assertEqual(txn_number, event.command["txnNumber"])
-        self.assertEqual(10, coll.count_documents({}))
+        self.assertEqual(48, coll.count_documents({}))
 
 
 class PatchSessionTimeout(object):