Debate about the epistemic prowess of historical science has focused on local underdetermination problems generated by a lack of historical data; the prevalence of information loss over geological time, and the capacities of scientists to mitigate it. Drawing on Leonelli’s recent distinction between ‘phenomena-time’ and ‘data-time’ I argue that factors like data generation, curation and management significantly complexifies and undermines this: underdetermination is a bad way of framing the challenges historical scientists face. In doing so, I identify circumstances of epistemic scarcity where underdetermination problems are particularly salient, and discuss cases where legacy data—data generated using differing technologies and systems of practice—are drawn upon to overcome underdetermination. This suggests that one source of overcoming underdetermination is our knowledge of science’s past. Further, data-time makes agnostic positions about the epistemic fortunes of scientists working under epistemic scarcity more plausible. But agnosticism seems to leave philosophers without much normative grip. So, I sketch an alternative approach: focusing on the strategies scientists adopt to maximize their epistemic power in light of the resources available to them.