A long literature on inter-distributional inequality (IDI) has developed statistical tools for measuring the extent of inequality between two groups (e.g. men versus women). The paper reviews some of the most prominent IDI indices proposed in the last four decades. The assessment focuses on how these indices react to inequalities that are disadvantageous to different groups, using two operationalizations of a concept of group-specific disadvantage focus (GDF). Relying on a complementary set of properties, the review also assesses whether these indices are informative about other interesting features related to IDI comparisons, chiefly distributional equality, but also absence of distributional overlap and presence of first-order stochastic dominance. The author proposes amendments to several of these indices in order to render them in fulfillment of GDF properties and more informative on the mentioned distributional features.