Outdoor Cat

I've gained a new friend - Smokey aka "Outdoor Cat". He can't live inside with me because I'd suffer horrible lung reactions... and so he gets the garage (cracked enough for him to get in and out) and the run of the large yard and woods. He's been guarding my yard for a few months now and I announced out loud a few days ago how happy I am that he doesn't have any hunter sensibilities. Not surprisingly, that very evening, while pulling into the driveway I noticed the carcass of a now deceased field mouse. I was told that I am supposed to praise him for this act, instead I announce "No Smokey! You killed Stuart Little". When discussing this with a friend the other day I was told that I'd should be happy he took care of it because having the rodent in the house is not a pleasant experience. I suppose this is true, but my animal loving side can't seem to get over the murder of this little furry guy.