diff --git a/tests/test_pool.py b/tests/test_pool.py
index d76e655e..0f664616 100644
--- a/tests/test_pool.py
+++ b/tests/test_pool.py
@@ -719,20 +719,31 @@ async def worker(pool):
     async def test_pool_max_inactive_time_05(self):
         # Test that idle never-acquired connections abide by
         # the max inactive lifetime.
+        connections = {}
+
+        async def init(con):
+            terminated = asyncio.Event()
+            connections[con] = terminated
+            con.add_termination_listener(lambda _: terminated.set())
+
         async with self.create_pool(
                 database='postgres', min_size=2, max_size=2,
+                init=init,
                 max_inactive_connection_lifetime=0.2) as pool:
 
-            self.assertIsNotNone(pool._holders[0]._con)
-            self.assertIsNotNone(pool._holders[1]._con)
+            # A connection may expire while the remaining connections are
+            # still being initialized, so observe termination from init().
+            self.assertEqual(len(connections), 2)
 
-            await pool.execute('SELECT pg_sleep(0.3)')
-            await asyncio.sleep(0.3)
+            await asyncio.wait_for(
+                asyncio.gather(*(event.wait()
+                                 for event in connections.values())),
+                timeout=5)
 
-            self.assertIs(pool._holders[0]._con, None)
-            # The connection in the second holder was never used,
-            # but should be closed nonetheless.
-            self.assertIs(pool._holders[1]._con, None)
+            for con in connections:
+                self.assertTrue(con.is_closed())
+            for holder in pool._holders:
+                self.assertIsNone(holder._con)
 
     async def test_pool_handles_inactive_connection_errors(self):
         pool = await self.create_pool(database='postgres',