I finally did it - just include following code to your functions.php:
/* Custom CSS styles on TinyMCE Editor */
if ( ! function_exists( 'myCustomTinyMCE' ) ) :
function myCustomTinyMCE($init) {
$init['theme_advanced_styles'] = 'Ueberschrift=ueberschrift;Foto=foto';
return $init;
}
endif;
add_filter('tiny_mce_before_init', 'myCustomTinyMCE' );
add_filter( 'mce_css', 'tdav_css' );
This not only removed all predefined classes from the dropdown box, but lets you declare your own classes within the tadv-mce.css file.
Only drawback: you will have to declare the classes you want to use within the "$init['theme_advanced_styles'] = 'Ueberschrift=ueberschrift;Foto=foto';" section of the code above. And naturally, your classes should also exist in your default-css for the frontend.
Also, if you have troubles with Safari/Mac, don't forget to empty your cache after doing any changes.