diff --git a/test/test_connection.py b/test/test_connection.py
index 16fbc9b20..6fb3ed042 100644
--- a/test/test_connection.py
+++ b/test/test_connection.py
@@ -215,30 +215,6 @@ class TestConnection(unittest.TestCase):
 
         self.assertRaises(TypeError, iterate)
 
-    # TODO this test is probably very dependent on the machine its running on
-    # due to timing issues, but I want to get something in here.
-    def test_low_network_timeout(self):
-        c = None
-        i = 0
-        n = 10
-        while c is None and i < n:
-            try:
-                c = Connection(self.host, self.port, network_timeout=0.0001)
-            except AutoReconnect:
-                i += 1
-        if i == n:
-            raise SkipTest()
-
-        coll = c.pymongo_test.test
-
-        for _ in range(1000):
-            try:
-                coll.find_one()
-            except AutoReconnect:
-                pass
-            except AssertionError:
-                self.fail()
-
     def test_disconnect(self):
         c = Connection(self.host, self.port)
         coll = c.foo.bar
diff --git a/test/test_threads.py b/test/test_threads.py
index dcf98fdc3..96de72141 100644
--- a/test/test_threads.py
+++ b/test/test_threads.py
@@ -296,26 +296,6 @@ class BaseTestThreads(object):
         error.join()
         okay.join()
 
-    def test_low_network_timeout(self):
-        db = None
-        i = 0
-        n = 10
-        while db is None and i < n:
-            try:
-                db = get_connection(network_timeout=0.0001).pymongo_test
-            except AutoReconnect:
-                i += 1
-        if i == n:
-            raise SkipTest()
-
-        threads = []
-        for _ in range(4):
-            t = IgnoreAutoReconnect(db.test, 100)
-            t.start()
-            threads.append(t)
-
-        joinall(threads)
-
     def test_server_disconnect(self):
         # PYTHON-345, we need to make sure that threads' request sockets are
         # closed by disconnect().
diff --git a/test/test_threads_replica_set_connection.py b/test/test_threads_replica_set_connection.py
index 01701bb98..b363c7b32 100644
--- a/test/test_threads_replica_set_connection.py
+++ b/test/test_threads_replica_set_connection.py
@@ -48,52 +48,6 @@ class TestThreadsReplicaSet(TestConnectionReplicaSetBase, BaseTestThreads):
         """
         return ReplicaSetConnection(pair, replicaSet=self.name)
 
-    def test_low_network_timeout(self):
-        """
-        Override the similar test as TestThreads.test_low_connect_timeout(),
-        but use the newer connectTimeoutMS and socketTimeoutMS arguments instead
-        of the soon-to-be-deprecated network_timeout.
-        """
-        db = None
-        n = 10
-
-        # First test connection timeout
-        i = 0
-        while db is None and i < n:
-            try:
-                db = ReplicaSetConnection(
-                    pair,
-                    replicaSet=self.name,
-                    connectTimeoutMS=1
-                ).pymongo_test
-            except AutoReconnect:
-                i += 1
-        if i == n:
-            raise SkipTest()
-
-        # ... then test socket timeout
-        i = 0
-        while db is None and i < n:
-            try:
-                db = ReplicaSetConnection(
-                    pair,
-                    replicaSet=self.name,
-                    socketTimeoutMS=1
-                ).pymongo_test
-            except AutoReconnect:
-                i += 1
-        if i == n:
-            raise SkipTest()
-
-        threads = []
-        for _ in range(4):
-            t = IgnoreAutoReconnect(db.test, 100)
-            t.start()
-            threads.append(t)
-
-        for t in threads:
-            t.join()
-
 
 class TestThreadsAuthReplicaSet(TestConnectionReplicaSetBase, BaseTestThreadsAuth):