A little twist to this question, but maybe don't think? When I was a teenager we would stand hunt the 1st weekend, then get a bunch of guys together and make drives. Easy to do back then because there was enough land and woods to go around. Its as changed from the past because now an 120 acre+ woodlot is now only enough for 1 or 2 people. But to continue, You often times didn't have time to think of the shot, just bring the gun, which has become an instinctive natural reflex, to your shoulder, swing on the running animal of choice and shoot it, not unlike like pass shooting a pheasant. For those that never had the chance to hunt pheasants in their backyard lets call it. like pass shooting a duck.
I love archery, still do and have taken my share, and missed my share, of rabbits. Once you get the knack of shooting a running rabbit with lead and all that goes with it, your just shooting instinctively and you may find you do that better than when something is sitting there and getting to your nerves. Btw, a recurve or long bow is what you want to use. You'll never be able to draw, hold, sight, holds some more, and shoot at something moving with a compound.
Now Im not advocating shooting at running game, but its what you did when driving deer or jumping on a brush pile for rabbits. To many times one sees the quarry way to soon and has time to think, way to much, hence my approach of not thinking at all.