The article assesses Will Kymlicka’s targeted approach to cultural rights by focusing on the case of the Roma minority in Europe. In Multicultural Odysseys, Kymlicka praises the European management of Roma issues as a promising way to overcome the flaws of the generic approach to cultural rights that dominates European minority rights otherwise. The article intends to evaluate Kymlicka’s statement in two ways : it combines an empirical study of the arguments that justify the institutional targeting of the Roma in the Council of Europe and a normative analysis about the specific type of transnational minority that these populations seem to form. The empirical part of the paper casts doubts on the assumption that cultural recognition matters primarily in the case of the Roma. The normative part of the paper argues that the concept of transnational minority gains more normative consistency when it is understood in terms of political mobilization against racial oppression than when it is justified in terms of cultural recognition. It concludes that Iris M. Young’s “politics of difference” provides a fruitful normative approach to make sense of the Roma’s claims of justice in Europe and that it is as such likely to refine and possibly complete the targeted to approach to multiculturalism.