We introduce a new model of stochastic choice, the “Progressive Random Choice (PRC) model.” In a PRC model, the decision maker randomizes over a collection of choice functions which are ordered with respect to some reference order. A PRC representation identifies the collection of choices and associated probabilities uniquely. Moreover, it can explain a rich set of stochastic choices. We are particularly interested in PRC where each choice function satisfies a well-known bounded rationality structure, namely “less-is-more.” The characterization of less-is-more-PRC relies on two simple axioms: U-regularity and weak-regularity. We further show that the reference ordering can be endogenously derived in this class.