add class to specific menu ul?

I know i can use:

function MYTHEMENAME_menu_tree(&$variables) {
  return '<ul class="MYCLASS">' . $variables['tree'] . '</ul>';
}

to alter every menu UL, but is there any way to specify one menu block menu only? or anything i can do to narrow it down at all? (i.e. it's the only block in the header)

thanks!