Rabbits... they run like their tails are on fire when I've got my bow in hand. They sit like statues when I'm toting a shotgun. Go figger.
I've hunted small game with my bow ever since I was a little kid and that's still my favorite hunting. Lots of shots, lots of action. Beats the tar out of sitting in a stand and trying to keep my eyes propped open.
I agree with TFOX, a recurve or longbow is the cat's meow when it comes to small game hunting. With a compound, I'd definitely take off the sights and shoot fingers. Being able to get on target and get the shot off quick is just as important as accuracy. In other words, MANDATORY.
Do not try for the classic heart/lung shot on rabbits. It's a small target and you're more likely to get a gutshot than anything else. A gutshot rabbit can make a clean getaway and wind up as coyote food. Go for headshots. Aim for the eye. A miss is a miss. A hit is a dead rabbit, or at least knocked cold as a cucumber so you can administer a coup de grace.
My favorite practice is just roving around and shooting at any worthy target of opportunity. I carry a plastic sack with me and pick off any coke/beer cans or plastic drink bottles I come across. Stick them in the sack when I retrieve my arrow. I hate litterbugs but I do enjoy the practice targets they leave me.