diff --git a/test/test_collection.py b/test/test_collection.py
index 5916ee60e..9ef3c2678 100644
--- a/test/test_collection.py
+++ b/test/test_collection.py
@@ -1460,12 +1460,9 @@ class TestCollection(unittest.TestCase):
 
         pipeline = {"$project": {"_id": False, "foo": True}}
         for result in [
-                db.test.aggregate(pipeline),
-                db.test.aggregate([pipeline]),
-                db.test.aggregate((pipeline,))]:
-
-            self.assertEqual(1.0, result['ok'])
-            self.assertEqual([{'foo': [1, 2]}], result['result'])
+                (db.test.aggregate(pl, cursor={})).next()
+                for pl in (pipeline, [pipeline], (pipeline,))]:
+            self.assertEqual({'foo': [1, 2]}, result)
 
     def test_aggregate_with_compile_re(self):
         # See SERVER-6470.
@@ -1478,10 +1475,10 @@ class TestCollection(unittest.TestCase):
         db.test.drop()
         db.test.insert({'r': re.compile('.*')})
 
-        result = db.test.aggregate([])
-        self.assertTrue(isinstance(result['result'][0]['r'], RE_TYPE))
-        result = db.test.aggregate([], compile_re=False)
-        self.assertTrue(isinstance(result['result'][0]['r'], Regex))
+        result = db.test.aggregate([], cursor={}).next()
+        self.assertTrue(isinstance(result['r'], RE_TYPE))
+        result = db.test.aggregate([], cursor={}, compile_re=False).next()
+        self.assertTrue(isinstance(result['r'], Regex))
 
     def test_aggregation_cursor_validation(self):
         # Regardless of version, should return CommandCursor when given
@@ -1491,10 +1488,11 @@ class TestCollection(unittest.TestCase):
         cursor = db.test.aggregate(projection, cursor={})
         self.assertTrue(isinstance(cursor, CommandCursor))
 
-        db = self.db
-        projection = {'$project': {'_id': '$_id'}}
-        cursor = db.test.aggregate(projection)
-        self.assertFalse(isinstance(cursor, CommandCursor))
+        if not version.at_least(self.db.connection, (3, 5, 1)):
+            db = self.db
+            projection = {'$project': {'_id': '$_id'}}
+            cursor = db.test.aggregate(projection)
+            self.assertFalse(isinstance(cursor, CommandCursor))
 
     def test_aggregation_cursor(self):
         db = self.db
diff --git a/test/test_database.py b/test/test_database.py
index ec4e895f5..90233d037 100644
--- a/test/test_database.py
+++ b/test/test_database.py
@@ -345,6 +345,8 @@ class TestDatabase(unittest.TestCase):
             raise SkipTest(
                 "Retrieving a regex with aggregation requires "
                 "MongoDB >= 2.3.2")
+        if version.at_least(self.client, (3, 5, 1)):
+            raise SkipTest("SERVER-24623")
 
         db = self.client.pymongo_test
         db.test.drop()
@@ -736,12 +738,18 @@ class TestDatabase(unittest.TestCase):
                               'count', 'test', maxTimeMS=1)
             pipeline = [{'$project': {'name': 1, 'count': 1}}]
             # Database command helper.
-            db.command('aggregate', 'test', pipeline=pipeline)
-            self.assertRaises(ExecutionTimeout, db.command,
-                              'aggregate', 'test',
-                              pipeline=pipeline, maxTimeMS=1)
+            if not version.at_least(self.client, (3, 5, 1)):
+                db.command('aggregate', 'test', pipeline=pipeline)
+                self.assertRaises(ExecutionTimeout, db.command,
+                                  'aggregate', 'test',
+                                  pipeline=pipeline, maxTimeMS=1)
+            else:
+                db.command('aggregate', 'test', pipeline=pipeline, cursor={})
+                self.assertRaises(ExecutionTimeout, db.command,
+                                  'aggregate', 'test',
+                                  pipeline=pipeline, cursor={}, maxTimeMS=1)
             # Collection helper.
-            db.test.aggregate(pipeline=pipeline)
+            db.test.aggregate(pipeline=pipeline, cursor={})
             self.assertRaises(ExecutionTimeout,
                               db.test.aggregate, pipeline, maxTimeMS=1)
         finally:
diff --git a/test/test_read_preferences.py b/test/test_read_preferences.py
index d193d029e..b4f947bbf 100644
--- a/test/test_read_preferences.py
+++ b/test/test_read_preferences.py
@@ -523,7 +523,8 @@ class TestCommandAndReadPreference(TestReplicaSetClientBase):
                 ('geoSearch', 'test'), ('near', [33, 33]), ('maxDistance', 6),
                 ('search', {'type': 'restaurant'}), ('limit', 30)])))
 
-        if version.at_least(self.c, (2, 1, 0)):
+        if (version.at_least(self.c, (2, 1, 0)) and
+                not version.at_least(self.c, (3, 5, 1))):
             self._test_fn(
                 True, lambda: self.c.pymongo_test.command(SON([
                     ('aggregate', 'test'),
@@ -568,8 +569,8 @@ class TestCommandAndReadPreference(TestReplicaSetClientBase):
         ])))
 
     def test_aggregate_command_with_out(self):
-        if not version.at_least(self.c, (2, 5, 2)):
-            raise SkipTest("Aggregation with $out requires MongoDB >= 2.5.2")
+        if not version.at_least(self.c, (2, 6, 0)):
+            raise SkipTest("Aggregation with $out requires MongoDB >= 2.6.0")
 
         # Tests aggregate command when pipeline contains $out.
         self.c.pymongo_test.test.insert({"x": 1, "y": 1}, w=self.w)
@@ -584,12 +585,14 @@ class TestCommandAndReadPreference(TestReplicaSetClientBase):
             warnings.simplefilter("ignore", UserWarning)
             self._test_fn(False, lambda: self.c.pymongo_test.command(
                 "aggregate", "test",
-                pipeline=[{"$match": {"x": 1}}, {"$out": "agg_out"}]
+                pipeline=[{"$match": {"x": 1}}, {"$out": "agg_out"}],
+                cursor={}
             ))
 
             # Test aggregate when sent through the collection aggregate function.
             self._test_fn(False, lambda: self.c.pymongo_test.test.aggregate(
-                [{"$match": {"x": 2}}, {"$out": "agg_out"}]
+                [{"$match": {"x": 2}}, {"$out": "agg_out"}],
+                cursor={}
             ))
         finally:
             ctx.exit()
@@ -662,7 +665,9 @@ class TestCommandAndReadPreference(TestReplicaSetClientBase):
 
     def test_aggregate(self):
         if version.at_least(self.c, (2, 1, 0)):
-            self._test_fn(True, lambda: self.c.pymongo_test.test.aggregate([]))
+            self._test_fn(
+                True,
+                lambda: self.c.pymongo_test.test.aggregate([], cursor={}))
 
 
 class TestMovingAverage(unittest.TestCase):