diff --git a/Doc/library/asyncio-eventloop.rst b/Doc/library/asyncio-eventloop.rst
index 75c459c0cb601f3..5627f0d54d32fde 100644
--- a/Doc/library/asyncio-eventloop.rst
+++ b/Doc/library/asyncio-eventloop.rst
@@ -1619,8 +1619,9 @@ Do not instantiate the :class:`Server` class directly.
       The sockets that represent existing incoming client connections
       are left open.
 
-      The server is closed asynchronously, use the :meth:`wait_closed`
-      coroutine to wait until the server is closed.
+      The server is closed asynchronously; use the :meth:`wait_closed`
+      coroutine to wait until the server is closed (and no more
+      connections are active).
 
    .. method:: get_loop()
 
@@ -1678,7 +1679,8 @@ Do not instantiate the :class:`Server` class directly.
 
    .. coroutinemethod:: wait_closed()
 
-      Wait until the :meth:`close` method completes.
+      Wait until the :meth:`close` method completes and all active
+      connections have finished.
 
    .. attribute:: sockets
 
diff --git a/Lib/asyncio/base_events.py b/Lib/asyncio/base_events.py
index 0476de631a6a525..416c732298d9a94 100644
--- a/Lib/asyncio/base_events.py
+++ b/Lib/asyncio/base_events.py
@@ -305,7 +305,7 @@ def _wakeup(self):
         self._waiters = None
         for waiter in waiters:
             if not waiter.done():
-                waiter.set_result(waiter)
+                waiter.set_result(None)
 
     def _start_serving(self):
         if self._serving:
@@ -377,7 +377,27 @@ async def serve_forever(self):
             self._serving_forever_fut = None
 
     async def wait_closed(self):
-        if self._waiters is None or self._active_count == 0:
+        """Wait until server is closed and all connections are dropped.
+
+        - If the server is not closed, wait.
+        - If it is closed, but there are still active connections, wait.
+
+        Anyone waiting here will be unblocked once both conditions
+        (server is closed and all connections have been dropped)
+        have become true, in either order.
+
+        Historical note: In 3.11 and before, this was broken, returning
+        immediately if the server was already closed, even if there
+        were still active connections. An attempted fix in 3.12.0 was
+        still broken, returning immediately if the server was still
+        open and there were no active connections. Hopefully in 3.12.1
+        we have it right.
+        """
+        # Waiters are unblocked by self._wakeup(), which is called
+        # from two places: self.close() and self._detach(), but only
+        # when both conditions have become true. To signal that this
+        # has happened, self._wakeup() sets self._waiters to None.
+        if self._waiters is None:
             return
         waiter = self._loop.create_future()
         self._waiters.append(waiter)
diff --git a/Lib/test/test_asyncio/test_server.py b/Lib/test/test_asyncio/test_server.py
index 06d8b60f219f1a3..7ff3f55f4f0c5ae 100644
--- a/Lib/test/test_asyncio/test_server.py
+++ b/Lib/test/test_asyncio/test_server.py
@@ -122,29 +122,59 @@ async def main(srv):
 
 class TestServer2(unittest.IsolatedAsyncioTestCase):
 
-    async def test_wait_closed(self):
+    async def test_wait_closed_basic(self):
         async def serve(*args):
             pass
 
         srv = await asyncio.start_server(serve, socket_helper.HOSTv4, 0)
+        self.addCleanup(srv.close)
 
-        # active count = 0
+        # active count = 0, not closed: should block
         task1 = asyncio.create_task(srv.wait_closed())
         await asyncio.sleep(0)
-        self.assertTrue(task1.done())
+        self.assertFalse(task1.done())
 
-        # active count != 0
+        # active count != 0, not closed: should block
         srv._attach()
         task2 = asyncio.create_task(srv.wait_closed())
         await asyncio.sleep(0)
+        self.assertFalse(task1.done())
         self.assertFalse(task2.done())
 
         srv.close()
         await asyncio.sleep(0)
+        # active count != 0, closed: should block
+        task3 = asyncio.create_task(srv.wait_closed())
+        await asyncio.sleep(0)
+        self.assertFalse(task1.done())
         self.assertFalse(task2.done())
+        self.assertFalse(task3.done())
 
         srv._detach()
+        # active count == 0, closed: should unblock
+        await task1
         await task2
+        await task3
+        await srv.wait_closed()  # Return immediately
+
+    async def test_wait_closed_race(self):
+        # Test a regression in 3.12.0, should be fixed in 3.12.1
+        async def serve(*args):
+            pass
+
+        srv = await asyncio.start_server(serve, socket_helper.HOSTv4, 0)
+        self.addCleanup(srv.close)
+
+        task = asyncio.create_task(srv.wait_closed())
+        await asyncio.sleep(0)
+        self.assertFalse(task.done())
+        srv._attach()
+        loop = asyncio.get_running_loop()
+        loop.call_soon(srv.close)
+        loop.call_soon(srv._detach)
+        await srv.wait_closed()
+
+
 
 
 @unittest.skipUnless(hasattr(asyncio, 'ProactorEventLoop'), 'Windows only')
diff --git a/Misc/NEWS.d/next/Library/2023-10-25-11-54-00.gh-issue-79033.5ePgFl.rst b/Misc/NEWS.d/next/Library/2023-10-25-11-54-00.gh-issue-79033.5ePgFl.rst
new file mode 100644
index 000000000000000..f131bf590870add
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2023-10-25-11-54-00.gh-issue-79033.5ePgFl.rst
@@ -0,0 +1,6 @@
+Another attempt at fixing :func:`asyncio.Server.wait_closed()`. It now
+blocks until both conditions are true: the server is closed, *and* there
+are no more active connections. (This means that in some cases where in
+3.12.0 this function would *incorrectly* have returned immediately,
+it will now block; in particular, when there are no active connections
+but the server hasn't been closed yet.)