I have used the chicken-wire set under a few inches of mulch for many, many years. It works great under my large azalea beds and other perennials. It's trickier to keep the varmints out of annuals, but have also used bits of chicken wire there.
Why on earth are people allowed to have 'pets' which invade their neighbors' yards, kill songbirds, and leave filth?!?! A trap sounds like a great idea to me!