diff --git a/test/asynchronous/test_cursor.py b/test/asynchronous/test_cursor.py
index 925584b89..833493ce3 100644
--- a/test/asynchronous/test_cursor.py
+++ b/test/asynchronous/test_cursor.py
@@ -1380,41 +1380,39 @@ class TestCursor(AsyncIntegrationTest):
         self.assertEqual("getMore", started[1].command_name)
         self.assertNotIn("$readPreference", started[1].command)
 
+    @async_client_context.require_version_min(4, 0)
     @async_client_context.require_replica_set
     async def test_to_list_tailable(self):
         oplog = self.client.local.oplog.rs
         last = await oplog.find().sort("$natural", pymongo.DESCENDING).limit(-1).next()
         ts = last["ts"]
-
+        # Set maxAwaitTimeMS=1 to speed up the test and avoid blocking on the noop writer.
         c = oplog.find(
             {"ts": {"$gte": ts}}, cursor_type=pymongo.CursorType.TAILABLE_AWAIT, oplog_replay=True
-        )
-
+        ).max_await_time_ms(1)
+        self.addAsyncCleanup(c.close)
         docs = await c.to_list()
-
         self.assertGreaterEqual(len(docs), 1)
 
     async def test_to_list_empty(self):
         c = self.db.does_not_exist.find()
-
         docs = await c.to_list()
-
         self.assertEqual([], docs)
 
-    @async_client_context.require_replica_set
+    @async_client_context.require_change_streams
     async def test_command_cursor_to_list(self):
-        c = await self.db.test.aggregate([{"$changeStream": {}}])
-
+        # Set maxAwaitTimeMS=1 to speed up the test.
+        c = await self.db.test.aggregate([{"$changeStream": {}}], maxAwaitTimeMS=1)
+        self.addAsyncCleanup(c.close)
         docs = await c.to_list()
-
         self.assertGreaterEqual(len(docs), 0)
 
-    @async_client_context.require_replica_set
+    @async_client_context.require_change_streams
     async def test_command_cursor_to_list_empty(self):
-        c = await self.db.does_not_exist.aggregate([{"$changeStream": {}}])
-
+        # Set maxAwaitTimeMS=1 to speed up the test.
+        c = await self.db.does_not_exist.aggregate([{"$changeStream": {}}], maxAwaitTimeMS=1)
+        self.addAsyncCleanup(c.close)
         docs = await c.to_list()
-
         self.assertEqual([], docs)
 
 
diff --git a/test/test_cursor.py b/test/test_cursor.py
index 26f0575da..e995bd529 100644
--- a/test/test_cursor.py
+++ b/test/test_cursor.py
@@ -1371,41 +1371,39 @@ class TestCursor(IntegrationTest):
         self.assertEqual("getMore", started[1].command_name)
         self.assertNotIn("$readPreference", started[1].command)
 
+    @client_context.require_version_min(4, 0)
     @client_context.require_replica_set
     def test_to_list_tailable(self):
         oplog = self.client.local.oplog.rs
         last = oplog.find().sort("$natural", pymongo.DESCENDING).limit(-1).next()
         ts = last["ts"]
-
+        # Set maxAwaitTimeMS=1 to speed up the test and avoid blocking on the noop writer.
         c = oplog.find(
             {"ts": {"$gte": ts}}, cursor_type=pymongo.CursorType.TAILABLE_AWAIT, oplog_replay=True
-        )
-
+        ).max_await_time_ms(1)
+        self.addCleanup(c.close)
         docs = c.to_list()
-
         self.assertGreaterEqual(len(docs), 1)
 
     def test_to_list_empty(self):
         c = self.db.does_not_exist.find()
-
         docs = c.to_list()
-
         self.assertEqual([], docs)
 
-    @client_context.require_replica_set
+    @client_context.require_change_streams
     def test_command_cursor_to_list(self):
-        c = self.db.test.aggregate([{"$changeStream": {}}])
-
+        # Set maxAwaitTimeMS=1 to speed up the test.
+        c = self.db.test.aggregate([{"$changeStream": {}}], maxAwaitTimeMS=1)
+        self.addCleanup(c.close)
         docs = c.to_list()
-
         self.assertGreaterEqual(len(docs), 0)
 
-    @client_context.require_replica_set
+    @client_context.require_change_streams
     def test_command_cursor_to_list_empty(self):
-        c = self.db.does_not_exist.aggregate([{"$changeStream": {}}])
-
+        # Set maxAwaitTimeMS=1 to speed up the test.
+        c = self.db.does_not_exist.aggregate([{"$changeStream": {}}], maxAwaitTimeMS=1)
+        self.addCleanup(c.close)
         docs = c.to_list()
-
         self.assertEqual([], docs)