Some considerations about the drowning of mice in a bucket of water:

This procedure may sound cruel, but in reality, it is not. In the autumn, as
the weather gets colder, rats and mice will move indoors  and stay there
until spring. Suppose you place a bucket of water, mixed with glycol, in the
attic/cellar; because of the admixture of glycol, the water will not freeze
if the temperature descends below 0 degrees C. The water/glycol mixture will
be very cold, and when the mice fall into it, they will, in a few seconds,
die of cold shock rather than by drowning. Used in this way, our mouse trap
is definitely not more painful for the mice than other traps...