We had mice in the house following the demise of our last cat. Used a humane trap baited with peanut butter with chocolate bits mixed in. It worked but then I read that you have to release them at least a mile from home or they just come back again. Mr Lead then got ruthless and bought some traditional spine-breaking traps, which worked all too well, indicating we had a problem - not just a solitary mouse that the cat brought in! We solved the problem by buying a plug-in device called a vermatik and kept it on every night for about 6 weeks as apparently this deterrent takes a while to be effective, in the meantime we continued with the traps, which eventually became redundant.