Assuming that you didn't use any questionable linking practices to get your site where it was before the penalty, I would submit the site for a manual review.
If you were using some gray hat tactics, you'll have a much better chance of getting rid of those links than the ones that were so generously pointed your way. So, you time would be better spent getting rid of the links you wouldn't want them to see that you actually built vs. trying to eliminate the ones that were likely sent by a competitor. The other alternative is to blame all of the bad links on the competitor...again, assuming that you built some links you don't want Google to see.
The other option, although more painful, is to wait it out. I've seen several sites get clobbered by competitor's nasty link building tactics and after a few months they all the sudden popped back into the SERPs higher than they were before hand.
The other thing I would suggest is to make sure those links are the source of your problem, i.e. how's your anchor text? Is it over optimized? How about on-site? And how could we forget good ole Panda and it's many, many revisions. Are you certain that it didn't get hit in the 2.14x update? (I'm kidding about the numbers...it just seems like Panda is never-ending.)