diff --git a/jupyterhub/app.py b/jupyterhub/app.py
index af394990..676198a6 100644
--- a/jupyterhub/app.py
+++ b/jupyterhub/app.py
@@ -930,7 +930,7 @@ class JupyterHub(Application):
 
         with an :meth:`authenticate` method that:
 
-        - is a coroutine (asyncio)
+        - is a coroutine (asyncio or tornado)
         - returns username on success, None on failure
         - takes two arguments: (handler, data),
           where `handler` is the calling web.RequestHandler,
diff --git a/jupyterhub/tests/conftest.py b/jupyterhub/tests/conftest.py
index c4c08b90..34c94e4f 100644
--- a/jupyterhub/tests/conftest.py
+++ b/jupyterhub/tests/conftest.py
@@ -55,10 +55,16 @@ _db = None
 
 
 def pytest_collection_modifyitems(items):
-    """add asyncio marker to all async tests"""
+    """This function is automatically run by pytest passing all collected test
+    functions.
+
+    We use it to add asyncio marker to all async tests and assert we don't use
+    test functions that are async generators which wouldn't make sense.
+    """
     for item in items:
         if inspect.iscoroutinefunction(item.obj):
             item.add_marker('asyncio')
+        assert not inspect.isasyncgenfunction(item.obj)
 
 
 @fixture(scope='module')