This paper develops the first operational tests of portfolio efficiency based on the general stochastic dominance (SD) criteria that account for an infinite set of diversification strategies. The main insight is to preserve the cross-sectional dependence of asset returns when forming portfolios by reexpressing the SD criteria in T-dimensional Euclidean space, with elements representing rates of return in T different states of nature. We characterize subsets of this state-space that dominate a given evaluated return vector by first- and second-order SD. This allows us to derive simple SD efficiency measures and test statistics, computable by standard mathematical programming algorithms. The SD tests and efficiency measures are illustrated by an empirical application that analyzes industrial diversification of the market portfolio.