This paper links governance reforms with potential improvements in efficiency in Spanish universities. Taking the classic DEA model as our starting-point, we focus on the study of efficient units to identify the ones that present atypical behaviour (outliers) and should be removed from the analysis, and then to order the remaining institutions in terms of what is known as robust efficiency. Moreover, we use a second stage regression analysis and a three- stage adjusted values non-parametric model to analyse the influence of environmental factors on the efficiency scores obtained. Once environmental factors are taken into account, the remaining unexplained inefficiency is attributed to governance failures. Our results indicate that the observed inefficiency in Spanish public universities is mainly determined by deficient governance. Thus, there is scope for improvements in efficiency through governance reform.