Excluding specific widgets from default sidebar class

Question

I have two sidebars using the register_sidebars function that display each widget as a list item with a class of .box:

<?php if(function_exists('register_sidebars')){

register_sidebars(2, array(
    'name'=>'sidebar%d',
    'id'  =>'sidebar',
    'before_widget'=>'<li class="box">',
    'after_widget'=>'</li><!--box--><!--aside-->',
    'before_title'=>'<h2>',
    'after_title'=>'</h2>',
));
}
?>

So the output goes something like:

<div class="side">
 <ul>
  <li class="box">
   <div class="textwidget">Lorem ipsum</div>
  </li><!--box--><!--aside-->
  <li class="box">
   <h2>Blogroll</h2>
   <ul class="xoxo blogroll">
   <li><a href="http://example.com">Example</a></li>
   </ul>
  </li><!--box--><!--aside-->
 </ul>
</div>

What I need is a conditional function so that any Links widget (or one with a class of .xoxo) in the sidebars will not get a class of .box because I want to style those and only those differently, and in a way that I can simply change certain styles from inside of .box. The main problem is that I don't know what function or variables to target with a filter. The codex doesn't do a good job of classifying less-used global variables and I can't see anything in the Filter Reference that looks like it should help.