This paper links the debates on constituent power and European independence movements in order to develop a theoretically compelling and empirically grounded conception of constituent power, as well as to assess in how far constituent power contributes to the meaning of political independence. In its first part, it builds upon recent republican contributions to the debates on corporate, joint and collective agency and argues that, even on individualist grounds, constituent power can convincingly be understood as a surplus of collective agency that corporate agency cannot encompass. In the second part of the paper, these preliminary theoretical considerations are confronted with the debates about Scotland's constitutional future and the 2014 independence referendum. This examination suggests further differentiation, but also facilitates insights into the interplay of the constituent power of the people with corporate forms of agency, as well as into changes of constituent peoples. In the final part, the paper inverts the perspective of inquiry to show that, once one is conscious of the complex relation between popular sovereignty and sovereignty that conceptions of corporate and collective agency help us to grasp, constituent power also proves to be an element of a compelling political conception of political independence.