My dogs can spring traps. Capture traps have not worked and are too large to put under the furniture where the mice like to run. I do not want to kill the mice just have them go away; however, disease from mice and their droppings is a bigger concern. Poison a neighbor put out almost killed another neighbors dog. The sticky traps also catch crickets and other insects. We have the manhole for the sanitary sewer in our backyard. They regularly clean/inpect it. The problem intensifies since they uncover the eroded soil from the cover. Yuck!
Although we live in town we get some interesting wildlife like the mountain lion that roams froom the golf course to the creek. We've had our outside pond fish disappear likely to be dinner for a possum. We've had a mallard nest under the tree; they are protected and the nest cannot be moved. That made up keep the dogs out of the backyard for several months. At least we do not have pigeons; we had a friend get deathly ill from pigeon poop on the window sills at school.; We've been visited by an owl large enough to carry off a small dog or cat. Unfortunately, as much as we want to protect oter species, sometimes it is not possible.
If you would like to have some of my varmits, I'll be happy to share.