We propose a two-stage procedure for finding realistic benchmarks for nonparametric efficiency analysis. On the first stage the efficient DMUs are figured out by a free disposal hull approach. These benchmarks are directly targeted by directional distance functions and the extent of inefficiency is measured along the direction towards an existing DMU. Two variants for finding the closest or the furthest benchmark are proposed. With this approach there is no need to use linear combinations of existing DMUs as benchmarks which may not be achievable in reality and also no need to accept slacks which are not reflected by the efficiency measure
