Can I display a category archive for a custom post type?

I've used CustomPress to create several custom post types; works great, and I have archives and single posts templates setup for each.

However: my custom post types share the global 'Category' and 'Tag' taxonomies. Is it possible to display an category archive for a single custom post type?

Ideally, my permalink would look like this:

mysite.com/custom_post_type/category/
(or, with dummy data:slight_smile:
mysite.com/vinyl/jazz/
mysite.com/compact_disc/jazz/

In the example above, 'vinyl' and 'compact_disc' serve as custom post types, and jazz is a global category. Right now I have a working category archive page for 'jazz' where all applicable post types are displayed; now i need to limit the category archive based on post type.