Baitcaster,

Putting a Cougar down does not require a .44 mag, but you want to have anough to stop them. 9mm or .357 should do the trick just fine.
Most important is that it is one you can shoot accurately under pressure!

I would strongly suggest not shooting the critter unless he offers you no other option, unless you want the meat/hide for your home.

Season closes on Mar. 15 ('04), so be sure you have a cougar tag in your possession; if not, you'll be explaining to the GW why you had to shoot the animal. If the critter is just watching you, get some distance between the two of you and make lots of noise in the process. Make him/her think you are HUGE (waving arms, etc.). A cougar is less prone to attack if he thinks he might lose the fight.

Don't try for head-shots...place a couple rounds right behind the front leg, low into the body cavity. That's where the heart is, and it generally offers a much better target...even if you miss the heart the lungs are right there with it. Shoulder shots, with enough gun, can knock them down long enough for a finishing shot...but you can also wind up with a wounded animal in the brush....and an irritated GW that has to go get it.

Want to avoid cougar's? Take a decent sized dog along with you...cougars are much less likely to approach any kind of canine....

(especially Huskies....:-)

Mike