wwpt, real simple...KEEP THE CAT INDOORS! It's been proven that cats that are allowed to roam freely outdoors have more health problems (eating things they shouldn't, fights with other cats, not to mention the breeding problem if they have not been neutered).
My cat has never been allowed to roam freely outside. She only goes to the vet and back in her carrier, and she is in excellent health! (shes 13 this year, and still going strong).
As for the mice, (and the rat I had this year in the subfloor of my mobile home), she thinks it's really neat watching them steal her kibble and secret it in the back of the pantry where they have a tendency to nest if the trap under the sink doesn't get them first. I have learned to just live with the rodent problem since moving to Pinon Hills, although this is the first year I have ever had a rat!