As seems to be the case most winters, we have mouse droppings starting
to pop up (or is it plop down?) in our basement.

Some judicious mouse trap use always stops the problem. But I'm
getting old and tired of the "standard" traps - baiting them, making
sure to not set them off myself, emptying the gross dead mice from
them, repeating...

(By "standard" I'm talking about the kind seen in Looney Tunes and
other cartoons - bait with cheese or peanut butter, and a piece of
metal snaps onto the mouse and kills it.)

What's a "better" mouse trap? By that I mean one that might kill
multiple mice without rebaiting, and that's easy to clean and reuse.

Not so fond of the bait traps that feed them poisoned food, as they
force me to figure out where the dead critters are. I'd rather
confine my looking for carcass hunting to where the trap(s) are.