query posts with 'cagetory__and' AND 'category__not'?

I’ve actually got two related questions, so thanks in advance for your help:

Part 1)
I’m currently using the following query:
$args = array('category__and' => array($cat1,$cat2), 'showposts' => 20 );
I would now like to EXCLUDE posts from a certain category, but adding a ‘category__not’ seems to negate the ‘category__and’. Is there a way to do both in a single query?

Part 2)
What if I want to make a category link that would take me to a list of posts including multiple categories, but excluding others (same as above, but without the custom query_posts template tag)?