Snap traps - the ones with metal bars and small plates to hold the bait, such as a piece of cheese - are safe around cats and dogs provided that you place the traps in places the pets can't reach, such as inside kitchen cabinets. The disadvantage is that you're going to have to deal with dead mice, and some of them manage to die in ways that are, frankly, messy. If you aren't squeamish, this works well.

If that doesn't sound appealing, Victor offers an electronic trap. Basically, this electrocutes the mouse. The Victor model is enclosed, so your pets can't get in there and hurt themselves.

Glue traps are messy, and I personally dislike them because they're a bigger hassle than the snap traps are. You can, however, use these around pets if you place them out of reach.

However, discouraging mice from hanging out in or near your home would be the best long-term solution. There are ultrasonic solutions, for example. Make sure that the model you look at doesn't affect any of the animals you want to keep around. Pet rodents, for example, can be affected by these devices. Rabbits can be affected, too...ours was, anyway, until we got rid of the device.

Rodent proofing is a good idea. You can do things like seal all of your food in plastic or glass containers to make it inaccessible to the rodents. We, for example, keep bread in Rubbermaid bread containers, which offer the extra advantage of keeping our bread fresher for longer.

Cleaning up immediately when you make a mess is another good deterrent. Mice just love to hang out in and near the kitchen, so be sure that this room in particular is exceptionally clean. They'll even get into the oven, when it's cooled off, to see if you've dropped a bit of food while pulling out a pan or tray.

Victor's Web site has other rodent-proofing solutions.

I am a fan of the mouse traps that do not kill. This assures me that there are no chemicals on or in them that my four little dogs could get sick from if they found it. You can find them at most big supermarkets in the extermination/trash bag area.

The structure of the ones I buy have a top that slides on and off so you can bait it, and later release the mouse at least 2 miles from your home. Basically, a mouse walks in the door by stepping on a ramp. Once the mouse has entered the trap, the ramp springs back up and the mouse cannot escape until you open the lid for him.