The performance of the widely used betting-against-beta (BAB) investment strategy is improved by controlling for the stochastic dominance (SD) relation between individual stocks and the market portfolio. Dominating stocks, preferred by all risk-averse and prudent investors, are excluded from the short leg of the BAB strategy. Stocks that are dominated by the market are excluded from the long leg of the strategy. This prefiltering significantly enhances a wide range of performance and risk measures including abnormal returns relative to various factor models. The improvements are especially pronounced for the third-order SD, are robust to transaction costs and different market conditions.