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). Firstly, I introduce the property of group-specific disadvantage focus (GDF). Indices satisfying this property are only sensitive to inequalities that are disadvantageous to one specific group. Then the paper reviews some of the most prominents IDI indices proposed in the last four decades. The assessment focuses on whether these indices satisfy GDF and, if not, how they react to inequalities that are disadvantageous to different groups. I also discuss whether these indices are informative, or not, regarding other interesting features related to IDI comparisons, e.g. distributional equality, absence of distributional overlap and presence of first-order stochastic dominance. Finally, I propose amendments to several of these indices in order to render them in fulfillment of GDF and more informative on the mentioned distributional features.