diff --git a/src/websockets/asyncio/messages.py b/src/websockets/asyncio/messages.py
index b57c0ca4..69636e3d 100644
--- a/src/websockets/asyncio/messages.py
+++ b/src/websockets/asyncio/messages.py
@@ -43,8 +43,7 @@ def put(self, item: T) -> None:
     async def get(self) -> T:
         """Remove and return an item from the queue, waiting if necessary."""
         if not self.queue:
-            if self.get_waiter is not None:
-                raise ConcurrencyError("get is already running")
+            assert self.get_waiter is None, "cannot call get() concurrently"
             self.get_waiter = self.loop.create_future()
             try:
                 await self.get_waiter
diff --git a/tests/asyncio/test_messages.py b/tests/asyncio/test_messages.py
index 2ff929d3..5c9ac944 100644
--- a/tests/asyncio/test_messages.py
+++ b/tests/asyncio/test_messages.py
@@ -37,14 +37,6 @@ async def test_get_then_put(self):
         item = await getter_task
         self.assertEqual(item, 42)
 
-    async def test_get_concurrently(self):
-        """get cannot be called concurrently."""
-        getter_task = asyncio.create_task(self.queue.get())
-        await asyncio.sleep(0)  # let the task start
-        with self.assertRaises(ConcurrencyError):
-            await self.queue.get()
-        getter_task.cancel()
-
     async def test_reset(self):
         """reset sets the content of the queue."""
         self.queue.reset([42])