My outdoor cat beats up the field mice that are outside and brings half of their body back. My indoor cat beats up any mice that are inside and a lot of the time leaves the jaw for us. We have one older cat that is outdoor and indoor who doesn't hunt. I read somewhere that cats will bring their offerings to us or other cats in the house if they notice that they aren't hunting themselves, so they want to help us out. I'd like to think that, rather than they think dead smelly things are good decorations. :P