diff --git a/docs/source/tutorial/getting-started/authenticators-users-basics.md b/docs/source/tutorial/getting-started/authenticators-users-basics.md
index 6726091ed..9c0c09eb0 100644
--- a/docs/source/tutorial/getting-started/authenticators-users-basics.md
+++ b/docs/source/tutorial/getting-started/authenticators-users-basics.md
@@ -130,7 +130,8 @@ By default, only the deprecated `admin` role has global `access` permissions.
 ## Add or remove users from the Hub
 
 :::{versionadded} 5.0
-`c.Authenticator.allow_existing_users` is added in 5.0 and enabled by default.
+`c.Authenticator.allow_existing_users` is added in 5.0 and True by default _if_ any `allowed_users` are specified.
+
 Prior to 5.0, this behavior was not optional.
 :::
 
diff --git a/jupyterhub/auth.py b/jupyterhub/auth.py
index aa200a513..4462f73a4 100644
--- a/jupyterhub/auth.py
+++ b/jupyterhub/auth.py
@@ -166,7 +166,8 @@ def check_allow_config(self):
             self.log.warning(
                 "No allow config found, it's possible that nobody can login to your Hub!\n"
                 "You can set `c.Authenticator.allow_all = True` to allow any user who can login to access the Hub,\n"
-                "or e.g. `allowed_users` to a set of users who should have access."
+                "or e.g. `allowed_users` to a set of users who should have access.\n"
+                "You may suppress this warning by setting c.Authenticator.any_allow_config = True."
             )
 
     whitelist = Set(