Adding CSS Classes to Widgets

I know that I can assign classes and unique IDs to Widgets via the following code:

register_sidebar(array(
    'before_widget' => '<div id="%1$s" class="widget %2$s">',
    'after_widget' => '</div>',
    'before_title' => '<h2>',
    'after_title' => '</h2>',
    ));

I also know that I can list all of the available Widgets via this code:

print_r(wp_get_sidebars_widgets());

But is there any way to add an additional CSS class to the ‘before_widget’ parameter to denote the Widget’s position? So that I might end up with…

<div id="linkcat-2" class="widget widget-1 widget_links"></div>
<div id="rss-2" class="widget widget-2 widget_rss"></div>
<div id="linkcat-16" class="widget widget-3 widget_links"></div>

As a client might add, remove or re-order Widgets within a sidebar, I want to avoid targeting a Widget via its ID within my CSS. I need to be able to style the first Widget within each sidebar.

Can anyone help or offer any ideas?