With rabbits I break their neck. I will see if I can describe how to do this.

Pick the rabbit up with your off hand (your left hand if you are right handed). Grab the rabbit in front of the hips, in that little hollow spot, and pick it up with its head hanging down toward the floor.

Use your other hand and grab the rabbits neck right behind the head.

Now you need to kind of "pop" the rabbits neck, pulling the snooter away from the tooter and twisting simultaneously.

I'm sure that there is a video of this someplace. I'll find one.