Some species of cat and dog are excellent mousers. Some are quite the opposite and have zero desire to chase or catch a rodent. In many cases the rodents are intelligent enough to actively avoid your pet, and they often travel and live in areas your pet cannot access. In some cases, the rodent is too large for your small breed pet. Overall, even the best mousers will help impact the rodent population, but you will still want to properly exclude your home and monitor traps in case the rodents get back in.