  In a classical optimal stopping problem the aim is to maximize the expected
value of a functional of a diffusion evaluated at a stopping time. This note
considers optimal stopping problems beyond this paradigm. We study problems in
which the value associated to a stopping rule depends on the law of the stopped
process. If this value is quasi-convex on the space of attainable laws then it
is a well known result that it is sufficient to restrict attention to the class
of threshold strategies. However, if the objective function is not
quasi-convex, this may not be the case. We show that, nonetheless, it is
sufficient to restrict attention to mixtures of threshold strategies.
