A method of stochastic dominance analysis with respect to a function (SDRF) is described and illustrated. The method, called stochastic efficiency with respect to a function (SERF), partitions a set of risky alternatives in terms of certainty equivalents for a specified range of attitudes to risk. It can be applied for any utility function with risk attitudes defined by corresponding ranges of absolute, relative or partial risk aversion coefficients. SERF involves comparing each alternative with all the other alternatives simultaneously, not pairwise as with conventional SDRF. Hence it yields a subset of the efficient set found by SDRF. Moreover, the method is readily implemented in a simple spreadsheet with no special software needed.