In the current European debate on how to tap the potential of data-driven innovation, data governance is seen to play a key role. However, if one tries to understand what the discussants actually mean by the term data governance, one quickly gets lost in a semantic labyrinth with abrupt dead ends: Either the concrete meaning remains unclear or when an explicit definition is given, it hardly describes the challenges, which are considered essential in this article, at least within the highly regulated EU Single Market. The terminological and conceptual ambiguity makes it difficult to adequately describe certain challenges for data governance and to compare corresponding solution mechanisms in terms of their conditions for success. This article, therefore, critically examines and further develops elements of data governance concepts currently discussed in Information Systems literature to better capture challenges for data governance with particular respect to data-driven innovation and conflicting interests, especially those protected by legal rights. To reach this aim, the article elaborates on a refined data governance framework that reflects practical experience and theoretical considerations particularly from the field of data protection and regulation of innovation. Against this background, the outlook briefly assesses the most relevant current draft laws of the EU Commission, namely: the Data Governance Act, the Data Act and the AI Regulation (especially the last one concerning the General Data Protection Regulation).