This paper provides a realist analysis of the EU's legitimacy. We propose a modification of Bernard Williams' theory of legitimacy, which we term critical responsiveness. For Williams, 'Basic Legitimation Demand + Modernity = Liberalism'. Drawing on that model, we make three claims. (i) The right side of the equation is insufficiently sensitive to popular sovereignty; (ii) The left side of the equation is best thought of as a 'legitimation story': a non-moralised normative account of how to shore up belief in (...) legitimacy while steering clear of both raw domination and ideological distortions. (iii) The EU's current legitimation story draws on a tradition of popular sovereignty that sits badly with the supranational delegation and pooling of sovereign powers. We conclude by suggesting that the EU's legitimation deficit may be best addressed demoicratically, by recovering the value of popular sovereignty at the expense of a degree of state sovereignty. (shrink)