ABSTRACT Sovereignty is a frequently used term when it comes to analyzing and shaping digital processes and transformations. For example, digital sovereignty has become a central concept in European politics in recent years. In this article, we argue that references to digital sovereignty have largely operated with an implausibly one-dimensional, overly simplified notion of sovereignty in general and its application to the digital in particular. We explore the question of what talking about sovereignty in the context of data and digital spaces can comprise. As a basis for this exploration, we distinguish three aspects of the concept of sovereignty: (1) sovereignty as absolute power, (2) sovereignty as embodied power, and (3) sovereignty as institutional power. We argue that, at least in the European debate on digital sovereignty, two of these aspects pertaining to the intricate relation between sovereign and addressee(s) of claims to sovereignty are consistently overlooked. Once understood as encompassing the three aspects distinguished above, digital sovereignty could be part of a normative framework that is normatively oriented towards vulnerability and freedom, that remains open and sensitive to tensions and ambivalences, and that continuously takes these as starting points for new approaches to governance and regulation of digital practices.