Standard accounts assume that representatives are authorised and held accountable through elections in territorially defined constituencies. In contrast, claims-making approaches hold that representation does not always depend on an electoral connection. This paper argues that the claims-making approach addresses some of the difficulties in the standard account, but remains itself theoretically underspecified. This becomes especially clear when applied to systems with exceptional institutional complexity like the EU. As an alternative to both those other approaches, the paper proposes a revised claims-making approach in which rights claims are used to specify representative claims. It then shows how rights claims do, indeed, play an important role in the representative claims that are made in the European Union arena, and how that, in turn, allows the Union to deal with some of the problems of applying standard forms of representation to its decision-making.