Here is my rule of thumb that has caused me to NEVER lose a wounded turkey (this is from almost two decades of shooting geese and ducks, and I use this rule with turkeys too):

If his head is down, he is down; if his head is up SHOOT HIS ASS AGAIN!

You will NOT catch a crippled turkey in a foot race. If he is flopping... let him flop... to hasten the process.. there are several things you can do: What I do with geese and turkeys is to stand on the head and grab the feet.. you gotta use two hands and be careful. With your foot on his head... pull up on the feet until you hear a deep, sharp POP. Then let him go cause he's already dead. Its important to keep the turkeys back TOWARD YOU! That way you cannot get spurred, and you cannot be flogged by wings.

As to grabbing him by the neck and spinning him like a goose.... thats not the way geese should be done anyhow... you gotta spin awfully hard to break the neck... and anyone who grabs a still living turkey by the neck and lifts him up is braver than I. Its a good way to get hooked right in the Easter basket. Also, if you are trying to save him for a mount... its about the worst thing you could do... if you think he is going to flop when you stand on his head... just wait 'til you try and lift him up....

My best friend has a decent method... he used a knife and finds the slit behind the ear and a quick jab.... lights out. Works on turkeys.

For ducks (phesants would apply too)..... I separate the last vertabrate from the skull... using God's own creation.. my canine tooth. For a pheasant, which isn't quite as hearty as a duck, I'd prbably just crush the skull with my thumb and forefinger like I do a dove.