Blawgletter's firm handles lots of patent infringement cases on a contingent-fee or hybrid basis. And by hybrid we mean either a fraction of hourly plus a contingent percentage, a flat-fee plus a kicker, or an hourly or flat fee with some case-specific incentive to get exceptional results.
Now we see a scholar who has looked at the market for lawyers who take on clients under a contingent-fee deal. Although it remains in draft form, we commend it to your consideration. See David L. Schwartz, The Rise of Contingent Fee Representation in Patent Litigation.