We tried a 'balance' trap (a live trap, where the weight of the mouse tips the trap, which causes the door to fall shut). We got one mouse with that; it was smaller than others we've caught (possibly a different species?), but otherwise unremarkable. In general, though, they seem to be able to take the bait from these traps too, without tripping them.
We've also tried glue traps. Either they're not going in these, or they're not getting stuck. Tonight, I'm going to add bait to the glue trap, so we'll at least know if they're going in there.
We don't want to use poison, because we have a couple of (fairly) lazy cats.
Suggestions would be appreciated.