This paper examines the sense in which rights can be said to exist. We examine various approaches to the definition and analysis of rights, focusing in particular on the compossibility of rights. Concentrating on three existing approaches to rights-social choice-theoretic, game-theoretic, and Steiner's approach-we suggest that rights are noncompossible in any interesting sense, that is, that the rights people have are nonexistent or vanishingly small. We develop an alternative account of rightswhich we claim is more in tune with moral intuitions-where compossibility is not important and rights cannot form the exclusive basis of morality or a theory of justice. Rights are constructed on the basis of more fundamental moral values. We demonstrate how they are constructed and the sense in which they exist even though they might not always be exercised, while acknowledging that rights that may never be exercised are hardly worth the name.