Number one, you want to, of course, kill the rabbit in the most humane way possible. Breaking the neck, while effective and quick if done properly, can be needlessly inhumane if not done with absolute precision every time. Instead, do this: Check around at the various grocery stores in your areas, starting with the biggest chain stores like Kroger, Tom Thumb, or whoever happens to be the Big Chain Store in your particular area and see if they sell dry ice. One of them will, you can be sure. Dry ice is quite inexpensive, especially when considering what it will do for you, and is usually sold by the pound. Simply run on down and get yourself a half pound or so, or if not that small a quantity, the smallest amount you can. Take it home and put the chunk of dry ice inside an escape proof enclosure. Some people say use a trash can with a lid, but I have found your average ice chest to be just fine. Set the ice on top of something high up in the chest so that the rabbit will not bump it and burn itself, but leaving enough room to close the lid. I use a cinder block. Gently place the bunny in the chest on one end, with the ice-laden object on the other, pour a small quantity, maybe half a cup, of water onto the ice and close the lid.
The bunny will breathe in the CO2 and essentially, just go night-night forever. There is no pain, only drowsiness, and sleep, according to my vet. Usually twenty minutes is sufficient for most rabbits, but use your best judgement. Obviously a flemish giant would require more than a regular.
Be careful not to use too much ice, because it can lower the body temp of the prey and potentially make locating it a problem for your burm.
I hope this helps. Please, try it and I think you will see the benefits to it.

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