Constitutional rights are often seen as invitations to engage in all things considered moral reasoning about how public authorities should act. The Impasse of Constitutional Rights challenges this widely accepted view by showing that it generates an irresolvable deadlock between rival theories of constitutional rights that share the same defects. This Element develops the alternative idea that rights-based constitutional order has its own distinctive moral project, which consists in rendering public authority accountable to the inherent rights of each legal subject. Taking this project seriously requires reconceiving the basic building blocks of rights-based constitutional order: justification, purposive interpretation, and proportionality. The resulting account both escapes the impasse to which the leading contemporary theories of constitutional rights succumb and expounds the normative connection between rights-based constitutional order and its most fundamental doctrines.