Widget Exceptions

Have a strange need on a project I’m working with.

In the functions.php form I have special styling/enclosure for the sidebar widgets:

<?php
if ( function_exists(‘register_sidebar’) )
register_sidebar(array(
‘before_widget’ => ‘<div class=”myclass”>’,
‘after_widget’ => ‘</div>’,
‘before_title’ => ‘<h2 class=”widgettitle”>’,
‘after_title’ => ‘</h2>’,
));
?>

So I have a Widget that I’m using on all pages in the same sidebar section. The difference is that I want to use a different enclosure around that specific widget. How can I do a conditional using the widget name, or what are my options?

Example that I’d change it to would be:

<?php
if ( function_exists(‘register_sidebar’) )
register_sidebar(array(
‘before_widget’ => ‘<div class=”myclass2″>’,
‘after_widget’ => ‘</div>’,
‘before_title’ => ‘<h2 class=”widgettitle”>’,
‘after_title’ => ‘</h2>’,
));
?>