This paper presents a solution to the problem of ranking efficient decision-making units (DMUs) in data envelopment analysis (DEA). We develop a cross-inefficiency approach for the deviation variables framework based on a pair of epsilon-based benevolent and aggressive models for both constant and variable returns-to-scale technologies. The new method improves the discriminating power of DEA, solves the non-uniqueness of ranking solutions, and avoids the negative efficiency scores associated with current models in the deviation variables framework. We illustrate the performance of the approach using a real-life case study. Not only does the research improve the discriminating power, but it also encourages the first step towards integrating the deviation variables framework in the context of decision-making uncertainty.