Has anyone hunted Cougar? (The cat type...not the human female type!)

One seems to have decided to take up residence on my north 40 and if I can't get rid of it any other way, I'll shoot it. (Legally, I have a couple of ways to do that.) So if it comes to it, I'd like to know if anyone has hunted them and how.

I went looking for sign today and found a kill (grown deer) in a little wooded glen about in the middle of the north 40. It had been picked clean, but it wasn't all that old. Of all the critters that could take up residence on my land, this is the one I'm least happy about. Too many instances of cougars thinking they're further up the food chain than we are, and I don't want it deciding that my kids or dogs look appetizing.