diff --git a/pymongo/asynchronous/mongo_client.py b/pymongo/asynchronous/mongo_client.py
index bfae302dac..4e09efe401 100644
--- a/pymongo/asynchronous/mongo_client.py
+++ b/pymongo/asynchronous/mongo_client.py
@@ -1453,13 +1453,6 @@ async def address(self) -> Optional[tuple[str, int]]:
                 'Cannot use "address" property when load balancing among'
                 ' mongoses, use "nodes" instead.'
             )
-        if topology_type not in (
-            TOPOLOGY_TYPE.ReplicaSetWithPrimary,
-            TOPOLOGY_TYPE.Single,
-            TOPOLOGY_TYPE.LoadBalanced,
-            TOPOLOGY_TYPE.Sharded,
-        ):
-            return None
         return await self._server_property("address")
 
     @property
diff --git a/pymongo/synchronous/mongo_client.py b/pymongo/synchronous/mongo_client.py
index 1351cb200f..815446bb2c 100644
--- a/pymongo/synchronous/mongo_client.py
+++ b/pymongo/synchronous/mongo_client.py
@@ -1447,13 +1447,6 @@ def address(self) -> Optional[tuple[str, int]]:
                 'Cannot use "address" property when load balancing among'
                 ' mongoses, use "nodes" instead.'
             )
-        if topology_type not in (
-            TOPOLOGY_TYPE.ReplicaSetWithPrimary,
-            TOPOLOGY_TYPE.Single,
-            TOPOLOGY_TYPE.LoadBalanced,
-            TOPOLOGY_TYPE.Sharded,
-        ):
-            return None
         return self._server_property("address")
 
     @property
diff --git a/test/asynchronous/test_client.py b/test/asynchronous/test_client.py
index c6b6416c16..590154b857 100644
--- a/test/asynchronous/test_client.py
+++ b/test/asynchronous/test_client.py
@@ -838,8 +838,6 @@ async def test_init_disconnected(self):
         c = await self.async_rs_or_single_client(connect=False)
         self.assertIsInstance(c.topology_description, TopologyDescription)
         self.assertEqual(c.topology_description, c._topology._description)
-        self.assertIsNone(await c.address)  # PYTHON-2981
-        await c.admin.command("ping")  # connect
         if async_client_context.is_rs:
             # The primary's host and port are from the replica set config.
             self.assertIsNotNone(await c.address)
diff --git a/test/test_client.py b/test/test_client.py
index 8e3d9c8b8b..5bbb5bd751 100644
--- a/test/test_client.py
+++ b/test/test_client.py
@@ -812,8 +812,6 @@ def test_init_disconnected(self):
         c = self.rs_or_single_client(connect=False)
         self.assertIsInstance(c.topology_description, TopologyDescription)
         self.assertEqual(c.topology_description, c._topology._description)
-        self.assertIsNone(c.address)  # PYTHON-2981
-        c.admin.command("ping")  # connect
         if client_context.is_rs:
             # The primary's host and port are from the replica set config.
             self.assertIsNotNone(c.address)
diff --git a/test/test_replica_set_reconfig.py b/test/test_replica_set_reconfig.py
index 1dae0aea86..4c23d71b69 100644
--- a/test/test_replica_set_reconfig.py
+++ b/test/test_replica_set_reconfig.py
@@ -59,7 +59,8 @@ def test_client(self):
 
         with self.assertRaises(ServerSelectionTimeoutError):
             c.db.command("ping")
-        self.assertEqual(c.address, None)
+        with self.assertRaises(ServerSelectionTimeoutError):
+            _ = c.address
 
         # Client can still discover the primary node
         c.revive_host("a:1")