Laying poison is a bad move. You can end up poisoning all sorts, especially the cat that's supposed to be catching the mouse, which as @wedge social points out, a cat is far from the dead cert killer we are all led to believe as kids! I have spotted mice before my cat.

We are the apex predator but we can be kind about infestations. Don't give pests a reason to move in. The place I live now was wasp infested, rat infested and ant heaven when I moved in. I haven't killed one and they have pretty much all gone.

For mice, block up gaps from outside. That tip about steel wool is a good one, or rolled up hardware cloth around entry points for pipes. They hate the smell of mint. I have a big bunch hanging up.

Don't leave food lying around.

I view cats as a deterrent, not a last line of defence. Have them for patrolling, putting rodents off settling down. And a dog patrolling too. We have a big hound it is a killer and the rats know it, another reason for them to keep out the way! A 35kg dog is no good for attic duty though :)

Last resort is humane traps to get them out and dropped off in a new locale. The thing is, we are the pest when we set up shop in a house in a field or equivalent. We can do better than just kill everything.