I've tried killing the mouse by taking it by the tail and slamming against a counter, but I wasn't very good at it and sometimes the mouse wasn't dead just not really alive either
(never thought of a bag or pillow case)
Another way, also by hand that works better for me, is to put a pencil or something behind the mouses neck (not with the point or back, but across, holding it down) and then you give a sudden pull on the tail. It breaks the neck and he is immediately dead.
But you have to be in for that of course. I myself don't mind killing them manually, as long as it is quick and painless.