That was enough for my wife to want a cat. We haven’t had any problems since and we live next to a horse pasture with a barn. A couple of years later we found a 2 x 6 ft hole in our house under our deck where they had nested and come in. Despite the hole, the cat didn’t let in any in the house.

Edit: I should add that I've always liked dogs and hated cats. But because the cat is so low maintenance and hunts mice, he's been pretty good.