Open data-sharing is a valuable practice that ought to enhance the impact, reach and transparency of a research project. While widely advocated by many researchers and mandated by some journals and funding agencies, little is known about detailed practices across psychological science. In a pre-registered study, we show that overall, few research papers directly link to available data in many, though not all, journals. Most importantly, even where open data can be identified, the majority of these lacked completeness and reusability - conclusions that closely mirror those reported outside of Psychology. Exploring the reasons behind these findings, we offer seven specific recommendations for engineering and incentivizing improved practices, so that the potential of open data can be better realized across psychology and social science more generally.