Display a single post category

Apologies if this has been addressed before – I tried to search around the forums for it, but it’s hard to condense the problem into convenient search terms.
I’m using the excellent Equilibrium theme, and I have it set so that only posts in a “Featured” category are displayed in the “Featured” section. So far, so good.
Now what I want to do is, by each post on the index, display the other category or categories it belongs to – in other words, a list of categories that excludes “Featured.” Is there any way to do this, short of using the_category and using PHP to find and cut out the “Featured” part of the string?
Thanks in advance for your help!