This paper proposes a refinement of the maxmin criterion for robust mechanism design and characterizes its implications in a canonical monopoly screening environment. In the model, a seller produces quality-differentiated goods to sell to a buyer of unknown payoff type. A mechanism is properly robust if it lexicographically maximizes expected profit with respect to a lexicographic probability system capturing first-order and higher-order uncertainty aversion about the buyer’s type. It is shown that a mechanism is properly robust if and only if it is efficient and revenue maximizing. That is, asymmetric information does not lead to economic inefficiency.