We use the mouse bucket in the shed on the side of our cabin, and in other outbuildings. We had a drum of olive oil that a mouse got into, which we could no longer use, so we put that in the buckets instead of water. It keeps the bodies from rotting so fast and stinking. It makes it so you don't have to mess with it that often. I don't know how well this would work in a forest setting. Other critters would probably get in the bucket, maybe tip it over, etc.
Used motor oil works as well. My father used to keep a 5 gallon bucket around for draining the oil out of tractors. After a few years when he finally emptied the bucket it was full of dead rats and mice. There was nothing to attract them to the bucket either. So it was just random passersby that fell in somehow. You would have never known they were in there, it didn't smell at all.
Yeah I was going to mention the motor oil, but knew that wouldn't work for Randy since he's certified organic. I had the same thing happen with an open pan of motor oil in my garage. You would never know they were in there. Its just like how the tar pits preserved animals.
I've used that method before, but dug a hole the size of the bucket into the ground, so the bucket was only 1 inch above ground level. Still catches mice/chipmunks, but larger animals can't tip it over.