If you have a pregnant woman in the household, you might not want to spread rat poison all over the place. And if you have a child in the house, you definitely don't want racumin dust all over the floor.

Snap-traps are messy. Avoid.

Cage traps are effective, but I don't know if they build them for smaller rodents. They have them for big rats.

Sticky traps are still the best. The Baygon stuff (with the yellow backing) is still more effective than most of the other products out there, as it's very difficult for the mice to escape. Bait it with something smelly. Lay down multiple traps in multiple locations... If a mouse hits one and manages to wriggle free, they will learn to avoid that spot from then on.

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One interesting way to trap mice that we learned about by accident? Having food waste at the bottom of a swing-top trash bin. Mice can get in... but they can't get out. Won't catch all of them, but ours caught a heck of a lot of mice back in the day.