Hi there.
I slit the throat but use a cone to restrain the bird and drain into a trash can. It's not messy but quite controlled. It also bleeds them out quite well.
Some folks will use a broomstick laid across the back of the neck and pull the legs for cervical dislocation. Many will accidentally pop the heads off. I tried this once and the cone was a better choice for
me. Note I only say once... and the first time I did the cone didn't go perfect either. No matter which method you try it will likely take some practice to get the SKILL honed in.
My grandma told stories about ringing necks... but that just seems challenging and maybe traumatizing to me as a keeper.
Since I am a one woman show... I have not tried restraining a chicken on a stump and swinging an ax for fear of taking my own leg off as I am highly prone to accidents. In fact, being afraid of cutting myself even hindered my first throat cutting... but the spine keeps the knife from going all the way through the neck.
I have seen folks using a cone and garden loppers instead of a knife. They take the head all the way off.
An alternative that creates restraint but less costly than cones is tying them up by their legs with a rope. I also tried that, but I have MORE control with my homemade cone... vinegar jug with top and bottom cut out.
Some folks will use Ether (carburetor starting fluid I think) to euthanize a bird inside an airtight bucket. I am unsure if this allows the meat to be viable for human consumption.
I'm sure there may be some methods I missed or didn't describe 100% accurately. Others will be along to share their experiences though. Help this help a little.
And congratulations on building the courage to reach the final step!
