Nutty Little Rabbits

Little bunnies are coming right up to the fence, and driving poor Pogi bonkers. Halo is used to them by now, but I just went out and talked to Pogi, with a rabbit munching plants 10 feet away. I'm trying to calm him down, but every fiber of his being wants to jump the fence and catch one. There is a local lady that "owns" all the wild cats and chickens, so maybe these are her rabbits as well. These are cottontails (rabbits), not the native jack rabbits (hares).

I was thinking of getting a pellet gun and shooting marauding birds, feral chickens and these pesky rabbits, but have mostly decided against it. It's true that these are pests, but I don't want to kill them.