diff --git a/telethon/client/auth.py b/telethon/client/auth.py
index 52d671ac..425789a9 100644
--- a/telethon/client/auth.py
+++ b/telethon/client/auth.py
@@ -147,14 +147,16 @@ class AuthMethods:
                 if bot_token[:bot_token.find(':')] != str(me.id):
                     warnings.warn(
                         'the session already had an authorized user so it did '
-                        'not login to the bot account using the provided '
-                        'bot_token (it may not be using the user you expect)'
+                        'not login to the bot account using the provided bot_token; '
+                        'if you were expecting a different user, check whether '
+                        'you are accidentally reusing an existing session'
                     )
             elif phone and not callable(phone) and utils.parse_phone(phone) != me.phone:
                 warnings.warn(
                     'the session already had an authorized user so it did '
-                    'not login to the user account using the provided '
-                    'phone (it may not be using the user you expect)'
+                    'not login to the user account using the provided phone; '
+                    'if you were expecting a different user, check whether '
+                    'you are accidentally reusing an existing session'
                 )
 
             return self