Open access to research data has been described as a driver of innovation and a potential cure for the reproducibility crisis in many academic fields. Against this backdrop, policy makers are increasingly advocating for making research data and supporting material openly available online. Despite its potential to further scientific progress, widespread data sharing in small science is still an ideal practised in moderation. In this article, we explore the question of what drives open access to research data using a survey among 1564 mainly German researchers across all disciplines. We show that, regardless of their disciplinary background, researchers recognize the benefits of open access to research data for both their own research and scientific progress as a whole. Nonetheless, most researchers share their data only selectively. We show that individual reward considerations conflict with widespread data sharing. Based on our results, we present policy implications that are in line with both individual reward considerations and scientific progress.