When I was a kid mom had us kill most of the roosters, since that was almost all we had. She didn't trust us kids with sharp objects, so we wrung their necks. After you whirl it and get some moment you sorta pop you wrist like you're flicking a towel at someone. The head stays in your hand and the body flops to the ground (and all over the ground). It's messy but quick once you get the hang of it, and works on even the toughest old birds. Very rarely would the head not snap off, but after the wrist pop is was dead regardless.
Mom told us later that she learned the same way of killing chickens when she was a kid.
Have to admit I made a point of being the one to kill the banty roo. He was bad to flog me when I wanted to tend my NH Reds. Really ticked me off. Never been so glad to kill a critter in my life.
When I watched Cold Mountain I rolled on the floor laughing at the rooster killing scene...