  We show that in Euclidean field theories that have bounce solutions, the
bounce with the least action is the global minimum of the action in an open
space of field configurations. A rigorous upper bound on the minimal bounce
action can therefore be obtained by finite numerical methods. This sets a lower
bound on the tunneling rate which, fortunately, is often the more interesting
and useful bound. We introduce a notion of reduction which allows this bound to
be computed with less effort by reducing complicated field theories to simpler
ones.
