This paper introduces a model to construct composite indicators for performance evaluation of decision making units, which is based upon the determination of the least distance from each assessed unit to a frontier estimated by data envelopment analysis. This generates less demanding targets from a benchmarking point of view. The model also makes it possible to account for the existence of slacks in all the considered dimensions (sub-indicators), playing with the notion of Pareto efficiency. Additionally, our approach satisfies units invariance, translation invariance and strong monotonicity and ensures that the weights used for the aggregation of the sub-indicators are always strictly positive. All previous approaches based on data envelopment analysis have failed to satisfy at least one of these properties. We also implement a new version of the Russell output measure of technical efficiency working with full-dimensional efficient facets. Finally, the new approach is illustrated by an application to the sphere of corporate social responsibility, showing the main empirical implications of the theoretical properties.