Many years ago, when we had a healthy pheasant population, my buddy's younger brother shot a nice ringneck. It folded and fell like a rock as soon as he shot. never making even a flutter. We walked over to look at it and congratulate him on a nice shot. He put the bird in his game pouch and we all spread out and resumed hunting. After walking a bit, I saw him jumping up and down, and frantically beating the back of his small game coat. I walked over to see what was going on. Just as I got to him, the ringneck stuck its' head out of the side of the game pouch, very much alive.
I quickly wrung its' neck, and put an immediate end to any suffering and further gymnastics. The head did not come off, but if it had, it still would have been quickly and humanely dispatched. I've finished a few other birds that way, and it takes far less time than using a knife or some blunt instrument. No tools necessary, just a quick grab and twist. Squeezing the sternum to suffocate or stop the heart sounds like a much slower death. Some guys make the mistake of killing the critter with the butt of their shotgun, and manage to break the stock in the process.