Defining custom ul class

Menu block's ULs are just generated using Drupal's standard theme_menu_tree(). So you can override that add classes to the UL.

This has put me in the right direction, but I was wondering if anyone could walk me through how to do this:

I would like to add 2 classes to ONLY the parent <*ul*> of ONE of Menu Block divs.

I put this into my template.php file:

function beckystheme_menu_tree($tree) {
  return '<ul class="menu nice-menu nice-menu-down">'. $tree .'</ul>';
}

That is working, it's just that is is being applied to EVERY ul, whereas I would just like the parent to get these classes. Also, I only want this to apply to ONLY one specific menu block (div#block-menu_block-4).

I understand I am missing a lot of logic in the function, but if some one could give me an idea hopefully I can figure it out. Thank you so much for your help and the great module.

Check out my patch, which adds the possibility of creating a wrapper template per level.