When I was a kid, my friends and I brought home hundreds of rabbits over the years, all killed with pellet guns. It's a good thing no one told us it couldn't be done, or we'd have missed out on a lot of good rabbit stew.
In those days none of us paid any attention to how many FPS a pellet gun was rated for, so maybe they used to make them more powerful back in the 80's than those sold today (without a PAL). I had a Crossman pump style gun that always resulted in a kill if pumped nine times and aimed at the head.