I think I've mentioned this before, but I got spooked on the "compression" (standing on the shoulder) technique when I was still learning to trap. Having read about this dispatch method, I tapped a fox on the head and stepped on top of him after he dropped to the ground. Suddenly, the fox came back to life and bit through both sides of my boot.
After that, I learned to tap them just a bit harder. I found that there is only a slight margin between the force required to render unconsciousness and that required to cause death. (But if you hit too hard you make your skinning job harder.) This is also true of humans, I understand, which makes the standard movie cliche of the hero getting knocked out by a blow to the head seem rather absurd. In actuality, the amount of force required to cause unconsciousness is only slightly less than that which would cause concussion or death. And that slightly lesser degree depends on a lot of variables. (Moral: don't ever try to knock someone out by hitting them on the skull with a hard object unless you are also prepared to kill them.) But now I digress.
The method I describe above only worked for me on fox. I wasn't able to dispatch a coon that way without creating an unpleasant skinning job, and resorted to using a .22. Now, most of my sets are made to dispatch the animal after the catch; I carry a .22 handgun in case of a live wolf or wolverine, which I will shoot through the heart/lung area.
Jim
Jim