Everyday clinical care generates vast amounts of digital data. A broad range of actors are interested in reusing these data for various purposes. Such reuse of health data could support medical research, healthcare planning, technological innovation, and lead to increased financial revenue. Yet, reuse also raises questions about what data subjects think about the use of health data for various different purposes. Based on a survey with 1071 respondents conducted in 2021 in Denmark, this article explores attitudes to health data reuse. Denmark is renowned for its advanced integration of data infrastructures, facilitating data reuse. This is therefore a relevant setting from which to explore public attitudes to reuse, both as authorities around the globe are currently working to facilitate data reuse opportunities, and in the light of the recent agreement on the establishment in 2024 of the European Health Data Space (EHDS) within the European Union (EU). Our study suggests that there are certain forms of health data reuse-namely transnational data sharing, commercial involvement, and use of data as national economic assets-which risk undermining public support for health data reuse. However, some of the purposes that the EHDS is supposed to facilitate are these three controversial purposes. Failure to address these public concerns could well challenge the long-term legitimacy and sustainability of the data infrastructures currently under construction.