This study is motivated by the important role that capital markets must play in financing a sustainable economy. We analyze the level of social responsibility of the companies included in and excluded from five sustainability indices compared to a control group of eleven conventional indices. In the period of study, June 2007 to June 2017, the level of social responsibility of all indices has improved. Our results show that the level of social responsibility is an important issue in the inclusion process and, to a lesser extent, in the exclusion process of the five FTSE4Good indices. However, we find similar results for several conventional indices. In addition, the size criterion predominates over the social responsibility in the inclusion and exclusion process of sustainability indices, similarly to conventional indices. Finally, using different cluster algorithms, we determine that the inclusion and exclusion process of four of five sustainability indices is different from that of the conventional indices. Our results support the use of the “sustainability” label by index providers, but also suggest that further differentiation between sustainability and conventional indices is needed.