If you really want the most humane trap possible then you have to live trap them and gas them with something heavier than air, like dry ice (CO2). This youtube guy made a pretty effective trap after testing a whole bunch of alternatives. It is a trap door that dumps the mouse in a bucket. Then you place some dry ice in the bucket or above it so the CO2 displaces the air, causing the mouse to go into hypoxia.
Alternatively you can fill the bucket with liquid and drown them or grab them with gloves and snap their neck. Which is still better than starving to death on a glue trap or being slowly played with until death by cat.
This trap is more effective than the spring traps, especially when you can trap multiple mice at the same time with the single trap. I've caught a over a dozen in the past year or two with it.
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