Abstract: In February, 2020, the European Commission published a white paper on artificial intelligence (AI) as well as an accompanying communication and report. The paper sets out policy options to facilitate a secure and trustworthy development of AI and considers health to be one of its most important areas of application. We illustrate that the European Commission's approach, as applied to medical AI, presents some challenges that can be detrimental if not addressed. In particular, we discuss the issues of European values and European data, the update problem of AI systems, and the challenges of new trade-offs such as privacy, cyber-security, accuracy, and intellectual property rights. We also outline what we view as the most important next steps in the Commission's iterative process. Although the European Commission has done good work in setting out a European approach for AI, we conclude that this approach will be more difficult to implement in health care. It will require careful balancing of core values, detailed consideration of nuances of health and AI technologies, and a keen eye on the political winds and global competition.