A recent paper by Hardaker et al. (The Australian Journal of Agricultural and Resource Economics, 48, 2004a, 253) and book by Hardaker et al. (Coping with Risk in Agriculture, 2004b) describe a procedure for determining an efficient set from among a set of random alternatives. This procedure, called stochastic efficiency with respect to a function (SERF), is claimed to make the same assumption concerning the risk aversion measures as does stochastic dominance with respect to a function (SDRF). This is claim is incorrect. SERF imposes an additional requirement on the risk aversion measures of the decision makers. Both procedures assume a lower and an upper bound on risk aversion, but SERF also assumes that all risk aversion measures are of the same functional form as these lower and upper bound functions. This additional strong requirement on risk preferences implies that the efficient set identified under SERF is usually smaller than that identified using SDRF.