If you think a dead rabbit would upset you.. there was a period of about 3 minutes where I was trying to figure out what the heck it was... after the fourth rabbit, Fuzzy and I came to an understanding about critters in the house.
Mole...yeah!!! kinda looks like a mole doesn't it? He leaves dead mice in the grass of a couple different houses in the neighborhood (including mine), same with birds... nothing is safe when he'* on duty.
I have a black cat identical to that one. He brings moles and chipmunks in and lays them next to his food dish. I guess he figures it'* a food exchange? The heads must be tasty, they are always missing. Unless the wife is getting to them before me.