Similarly, how are you with ferrets?
We had a rat problem, got two ferrets, and the rats moved out on general principle. Works best if you give the ferrets the run of the house every once in a while so the predator scent properly wards the premises.

It's so funny thinking of rodents being afraid of ferrets. They'd likely play with the rats rather than hurt them. It's like mistaking a pug for a timberwolf. Awww, so cuuuuute! :)