I was once a believer, but usually, there is never 'just one mouse'.
For anyone (respectfully) who has passed the "they're so cute, catch and release" stage either by sheer numbers of mice or their poopage, or, if you need to leave a trap for awhile and feel killing them quickly is in this case the more humane route, there is another alternative. Victor, the company that makes exterminator products for the home, has an electric trap (4 AA batteries) that is supposed to kill them instantly, and it works very, very well. They're $20 at Home depot for the mouse model, you just put the bait, either what they like at your house or say peanut butter and you're done. When they go far enough into the box, they get zapped and are easy to remove. Dry bait such as birdseed or dog food kibble are often better as peanut butter may be messy to clean out.
If you do catch and release, try to be wise about not releasing too far out of their local area because you may be passing insect vectors that carry pathogens from one colony/area to the next without knowing it.