If you had some chickens, catch the mouse in a live trap, throw the mouse to the chickens, then watch nature take its course.
http://www.youtube.com/watch?v=bGcgDO_pe2M
like this?
They sure evolved quite a bit from dinosaurs but pack hunting instincts are still the same.
I had a previous home which was above a forest full of wild animals but I didn't get rats, only those carried by the cat (rare, they usually ate them). Actually there was one once that nested in the low floor (probably got in through the door that was open all the time) but that was it. The momma rat just fell off the terrace and died, while the pink sqeaking pieces of meat were eaten alive by my cat. I could hear the bones crushing while they were still squeaking.
There are no light wooden suburbia houses here so it's unusual to have rats inside houses. It's all rock, brick or cement with foundations and no gaps or entrances.
I think the effectiviness of cats depend on the kind of cat.
Indoor domestic cats (life span: 14+ years): they're kids forever, they're well fed so it's just predatory instincs and play, they care about you so they want to bring you gifts.
Farm/outdoor cats (life span: 4-7 years): semiwild, don't have much of a relationship with the owner, they don't always have food available if other cats ate everything already, they will hunt for food.