I don't have mice here, but down in Mojave there are plenty at the test sites, and you want them gone because the natural predators they attract have poisonous fangs.

You can get a little plastic tube, bent in the middle like a banana. The far end is baited, and when the mouse goes in, the tube tilts and a propped door shuts. The rodent then gets a free ride to some distant location and dumped. Some ads say to dump the whole trap in the trash and forget it, but that's just nasty. Not as nasty as glue traps, but nasty.

I do have rats here on rare occasions, and a live-catch cage trap (I have them in three convenient sizes from Rat up to Raccoon) is used for that.

I have used poison when the traps didn't work, and I was getting things chewed in my attic, including electrical wires.