Exclude Categories from category_link

I’m trying to place a link to a post’s category on its single.php page. Easy enough, but my problem is that some of the posts will be in two categories (the second is just to make it easy to place it in a “featured” area on the homepage).

The code I’m using now:
<a href="<?php echo $category_link; ?>" title="Category Name"><?php the_category(); ?></a>
will display all categories.

Is there a way to exclude certain categories from this? I’ve tried a few of the usual things but, as php is by no means my specialty, I’m having some trouble with this.

Thanks for any help anyone can offer.