A major drawback of Mean-Variance and Stochastic Dominance investment criteria is that they may fail to determine dominance even in situations when all “reasonable” decision-makers would clearly prefer one alternative over another. Leshno and Levy [1] suggest Almost Stochastic Dominance (ASD) as a remedy. This paper develops algorithms for deriving the ASD efficient sets. Empirical application reveals that the improvement to the efficient sets implied by ASD is substantial (64% reduction for FSD). Direct expected utility maximization shows that investment portfolios excluded from the ASD efficient set would not have been chosen by any investors with reasonable preferences.