Optimization Letters, v. 12, n. 5, pp. 1029–1044. Abstract: In some cases, decision making units have a two-stage structure, in which the first stage uses inputs to produce outputs that are subsequently used as inputs for the second stage. This paper departs from previous two-stage data envelopment analysis by proposing a new combined model, based on directional distance function, that improves the accuracy of the efficiency scores under constant returns to scale production technologies. We compare the proposed model with the existing ones in the literature by means of a numerical analysis, showing its applicability.