The Persian ibex, however, was a stunning success - so much so that female ibex hunts are held today to keep the population in check. The Persian ibex, actually not a true ibex but a wild goat, was released in the Florida (pronounced as the Spanish: flor-ee-da) Mountains south and east of Deming, NM. This is a rugged mountain range about 20 miles long and only a single ridge-crest wide at the top, with many cliffs perfectly suited for ibex.
I personally accompanied ibex hunters in these mountains for about 10 years and believe this is a unique hunting opportunity in the US. Trophy size is as good as or better than in Iran (the world record horns are from this US herd), and special opportunities exist for muzzleloader and archery hunters. The best chance for success is, of course, the once-in-a-lifetime, either-sex, any firearm hunt, but the odds of drawing that tag run about 1:200. However, New Mexico's draw system is set up so that if your application is drawn, they will consider any of your first three choices before moving on to another hunter's application. Therefore, if you are willing to try the hunt with a muzzleloader, the odds improve significantly (around 1:42). New Mexico excludes ibex (and oryx) permits from resident/nonresident quotas, so all applications in the pool receive equal consideration.