Only in .: nice_menus-menu_name_class.patch
diff -rup ../nice_menus/nice_menus.module ./nice_menus.module
--- ../nice_menus/nice_menus.module	2010-08-17 15:54:44.000000000 +1000
+++ ./nice_menus.module	2010-08-18 14:48:04.320454681 +1000
@@ -481,7 +481,7 @@ function theme_nice_menus($id, $menu_nam
 
   if ($menu_tree = theme('nice_menus_tree', $menu_name, $mlid, $depth, $menu)) {
     if ($menu_tree['content']) {
-      $output['content'] = '<ul class="nice-menu nice-menu-'. $direction .'" id="nice-menu-'. $id .'">'. $menu_tree['content'] .'</ul>'."\n";
+      $output['content'] = '<ul class="nice-menu nice-menu-'. $direction .' '. $menu_name .'" id="nice-menu-'. $id .'">'. $menu_tree['content'] .'</ul>'."\n";
       $output['subject'] = $menu_tree['subject'];
     }
   }