Natalie, mouse traps are inexpensive and relatively safe for anything coming in contact with them other than mice - including human fingers. Peanut butter is your friend :)

"Traps are often preferred over poison baits for the following reasons:

Poison baits can harm children, pets and non-target animals.
Sick rodents may escape to areas between walls or under floors where they die and decompose, causing odor and insect problems.
Traps are often especially preferred for controlling easy-to-trap mice, since they eat less than rats and sometimes do not ingest enough rodenticide to make it effective. "

Please believe #2, or I'll have to describe what happened when a neighbor tossed some of the clean-and-easy-to-use envelopes of bait under her side porch :)

Thank you Morz8,

I am going to Home Depot today to stack up on traps.
Thank you for NOT describing what happened to your neighbor's mice. I just ate :-).

I think these are rats in my yard, not mice. My husband said he saw mice, they look much smaller then our present tenants.

We had a rat problem on our attic few years back, and the professional pest control company took care of it. It's funny how the houses are being built: they leave a space between the roof and the wall for "ventilation purposes" and saving the cost, so squirrels, mice and whatever creature can get there - makes a house up on the attic. So, we had to cough up few thousand dollars to build a special metal net for protection. Rats are gone from inside - thank goodness, but there are so many of them outside suddenly!
Anyway, I am just venting.
The apprehension with traps I have is that I will have to wait till they die - yuck! And then dispose them...
OK, time to shop.
~Natalie

'fat mouse with a short tail' sounds like a vole, to me.

Rats are quite big and have a long, naked (no fur) tail. If your mice have short tails they are likely voles.

Trying to remove voles from the outdoors is futile. No matter how many you trap, more will soon move in. There are substances that you can put on plants which make them taste bad.

See link below for more details

Here is a link that might be useful: Meadow voles

I also think you are seeing voles. They are just different enough looking from a house mouse or a baby rat, many people have gazillions of them and don't even know it. I felt positively idiotic when I saw this cute little round creature in broad daylight sitting in a flower bed eating. It was a round as a cue ball, tiny tail and just as cute as a button. I actually sneaked up to it and took a picture and then got on the inet to see what kind of rodent it was. rofl. OMGosh, I took a picture of a vole and didn't even know it, although I can identify vole damage with my eyes closed. Very embarrassing.

Controlling voles are a pipe dream. The good news is, they normally stay outside.

You can control voles. In fact I do. I had a horrendous vole problem last summer and into fall and winter. They ate my potatoes, all my fall/winter beets and carrots and through the winter ate all my lily bulbs. But here's what really works.

First find the holes they come out of. This is much easier when the foliage is gone from the garden. Determine if it's an active hole by placing a piece of apple in front of the hole. On either side of the hole put down two short pieces of 2x4. Place a bucket over them and weight it down with a rock. (This keeps rabbits or squirrels from taking the apple, and you'll use this set up repeatedly.) If the apple disappers, it's voles. Now, here comes the control part. Put some mouse poison in a yogurt or cottage cheese cup and put it under the bucket set up, facing the hole. The bucket set up keeps it safe for your pets and other animals. Check it regularly and replace as needed. You can do several holes at a time.

Believe me, this is safe--I have three dogs and a cat--and it works. I'd have no garden by now if I'd ignored the voles. They reproduce year round.

I bought large rat traps, and we cought several rats and a mouse. It was discusting to remove them, so we disposed the dead bodies along with the traps.
There are voles and rats. I see huge holes in my flower beds, and accused chipmunks, since there were lots of them. Though some of the holes are rather big, so it must be voles. Lots of lily bulbs I have planted did not even show up - must have been eaten by the beasts. Many (most) lilies have been bitten off at the base, and I saw a rat chewing on the leaves. I have never seen as many rats outside - maybe it is a drought, they come around the water hose.
Thank you all for good advice.
Laceyvail , I will give your bucket test a try later in fall when all the foliage is gone and I can clearly see the holes. Do they smell as bad as rats when they die? Will it affect birds and other animals who might eat the dead bodies?
Davidandkasie, BB gun and beer? Sound tempting, but my neighbors might call 911. At this point I am ready to try anything. Wish we could have cats, but my DH is allergic to them. I planted catmint for the neighbor's cat who comes around sometimes.
My husband said if he sees another rat, he will put this house on a market. And he is not kidding - rats and snakes are his "least favorite" of all the animal kingdom.

Natilie,
If you do end up moving to a place without rats, let me know where it is! The only places I can think of that might be ratless are the Artic and Antartic.

I'd reconsider cats, if I were you, and you're not the type of person who embarrasses easily. There are those hairless cats, which don't have dander to cause an allergic reation to your DH. (Also, sometimes folks allergic to cats, can tolerate the symptoms, if the cat has short hair.)

Also, since you live down south far enough that winters aren't a terrible problem, you can always keep the cat outside. (I doubt that's a good idea for the hairless cat, since they would have trouble keeping warm on a chilly night.)

The only problem with getting a cat is getting a "mouser." Unless a cat is trained well as a kitten, it won't be much help. My old cat enjoyed "raw" mice, squirrels, rabbits, and birds, with the only evidence leftover was finding a squirrel tail or a small pile of feathers in the yard.

Well, OK, so there were several incidents of him giving us his wonderful prizes of live or dead critters at our feet inside. (Always amused me that he became just my cat again, when DH got the present.) Poor cat, never got the gratitude he was expecting by giving us his most precious gifts, but it's hard catching a flying sparrow indoors!

Oh, and David,
You sound like my roommate's hubby -- he'd do the same thing with a rifle, after work, to "hunt" for deer. They lived on a farm, so the corn field across the driveway was a perfect place for deer to eat -- and die. LOL