We live within just a few feet of a patch of woods. Before we got our cats, every time the weather would change, mice would come in the house.
Someone told me that if you put poison out for them, that the chemicals in the poison would keep them from stinking after they died. In other words, the mouse could be in the wall, but you'd never smell it. That sounded like a good plan, so we bought some poisonous baits.
Unfortunately, that person was misinformed, because the end of our hall REEKED of "dead mouse" for a couple of weeks. Gaak. But what REALLY changed my mind about the poison was when we found a dead mouse in the floor at the foot of our bed one morning. It was in horrible physical shape from the poison, and it was obvious that it had suffered for a long, long time. I felt terrible.
I've never used them, but I've heard those sticky traps prolong suffering as well.
Mice don't even come into the house now that we have cats (I guess the mice smell them), but if we did need to get rid of any, we'd just use traditional mouse traps. At least those usually work instantly.