Further to the shouts for poison, poisoned mice will not die in the cavity wall, or under the floorboards and stink the house out. Yes, they will die, and quite likely to be in those areas, but dead meeses desiccate, not rot, so there is no smell attained for your victorious rebuffal of the invading hordes.
Dead rats, however, DO rot, and DO stink and will ensure a further invasion of bluebottles and other winged pests. So they always have a little dying "up yours" to impart. The bastards.