diff --git a/minode/tests/test_network.py b/minode/tests/test_network.py
index dbf5bc3..47b405a 100644
--- a/minode/tests/test_network.py
+++ b/minode/tests/test_network.py
@@ -127,19 +127,28 @@ class TestNetwork(unittest.TestCase):
                 else:
                     return 'Spent too much time trying to connect'
 
-        def time_offset_connections(nodes, offset):
+        def time_offset_bad_connections(nodes, offset):
             """Spoof time.time and open connections with given time offset"""
             with time_offset(offset) as time_call:
                 result = try_connect(nodes, 200, time_call)
                 if result:
                     self.fail(result)
 
+        def time_offset_good_connections(nodes):
+            """Connect to at least one node with acceptable time offset"""
+            with time_offset(-3500) as time_call:
+                result = try_connect(nodes, 200, time_call)
+                if not result:
+                    self.fail('Failed to connect with acceptable time offset')
+
         self._make_initial_nodes()
         nodes = random.sample(
             tuple(shared.core_nodes.union(shared.unchecked_node_pool)), 5)
 
-        time_offset_connections(nodes, 4000)
-        time_offset_connections(nodes, -4000)
+        time_offset_bad_connections(nodes, 4000)
+        time_offset_bad_connections(nodes, -4000)
+
+        time_offset_good_connections(nodes)
 
 
 class TestConnection(TestProcessProto):