If you are hunting rabbits, it is best to watch them a while before shooting. If they stagger around like they are drunk or disoriented, they may have tularemia. They contract it by eating their own poop, which can be contaminated by ground contact. Pigs contract it frequently as well.
I usually sit outside in the morning with a cigarette, and watch them scamper all over the place. I don't hunt them. I'll keep an eye out for funny looking critters, though. We have Red Tail Hawks and Kestrel Hawks patrolling the air. They'll pick off the sick ones.