How to use nice_menu to theme active menu

Hi,

I would like to use nice menus to theme part of the active menu tree, so that the menu displayed is context-sensitive. I guess I would need to do something like the following pseudocode:

 $id = get id of current active menu;
 $tree = get tree starting from level 3 of $id;
 print theme('nice_menu', $tree, 'down');

Is something like this possible?

Thanks

Chris