An old cat hunter gave me a tip about eating cougar. He said to leave the cat treed for a while to let it sort of calm down after the chase. Then vaporize it's head with a rifle shot to kill it instantly. He claimed the meat tasted better after doing it that way as opposed to the old method of shooting a treed cat in the lungs with a 22 mag and letting it fill up with blood and falling out of the tree a few minutes later.
I can't vouch for any of that info personally. I won't eat cat.