This article investigates the Stochastic Dominance (SD) of investment strategies which combine a long position in a stock index with a short position in options written on that index. Two main issues are analysed here: First, exercise prices are analysed which are conditioned on proxies of expected returns. Second, next to the well-known covered call strategies, the SD of uncovered put strategies is also investigated. Empirical analysis of strategies on the Dow Jones EURO STOXX 50 Index shows that covered call strategies dominate an index investment at the second and third degrees, while uncovered put strategies fail to do so. It can be observed that strategies with conditional exercise prices are stochastically dominant to strategies with unconditional exercise prices.