Free: Contests & Raffles.
Might consider cougar for meat hunting too.
The "official" response is in from DFW: "Reality is that cats kill few if any bighorn sheep in this area." The biologist said the Clemans sheep herd is "almost too healthy" and they've relocated over 200 of them to other areas, and will be increasing the number of ewe tags this year to help control the population. He said "hunting is very unlikely to have any impact on cat populations," so if that's what you're into, hunt away!
They're really gutsy when it comes to exiting the woods. Not nearly as bad as wolves. Never heard of a cougar killing for sport.