By establishing a common data governance mechanism across the EU, the Regulation on the European Health Data Space (EHDS) aims to enhance the reuse of electronic health data for secondary use (e.g. public health, policy-making, scientific research) purposes and realise associated benefits. However, the EHDS requires health data holders to make available vast amount of personal and non-personal electronic health data, including electronic health data subject to intellectual property (IP) rights, for secondary use, which may pose risks for stakeholders (patients, healthcare providers and manufacturers alike). This paper highlights some conceptual legal problems which need to be addressed in order to provide clearer regulatory requirements to ensure effective and consistent implementation of key data minimisation measures (anonymisation or pseudonymisation) and data management safeguards (secure processing environments). The paper concludes that the EHDS has been drafted ambiguously (for example, its definition of “electronic health data” or the list of “minimum categories of electronic data for secondary use”), which could lead to inconsistent data management practices and may impair the rights and legitimate interests of data subjects and rights holders. To address legal uncertainties, prevent fragmentation and mitigate/eliminate risks, the EHDS requires closely coordinated implementation and legislative fine-tuning.