Hi Jochen,
In the template which you are using , select the "Alert" for which you want to configure the notification.
Under notification tab, you have 3 ways ( Active, Template, Inactive ).
1. Active = You don't want to use the global defaults as well as template defaults. You can add your own desired recepients when you select this option.
2. Inactive = Don't want notifications
3. Template Settings = Template defaults
Settings made at lower level of the hierarchy overrides the higher level.
Hope this helps.
Regards,
Manish