The COVID-19 pandemic has been the scene of several epistemic battles at the science-society interface, creating deadlocks that have been hard to overcome. To cut through the paralysing elements of these discussions, we present an analysis of three epistemic battles, concerning empirical evidence, expertise, and model projections. Our analysis singles out a crucial factor that drives unhelpful disputes like these: the contested prioritisation of specific types of scientific knowledge, which are considered adequate for policy only if they meet predetermined standards. To move beyond these deadlocks, we introduce the conceptual tools of epistemic pluralism and contextualism, which give concrete indications in the three controversies we discuss and show us the way forward in debates on science-based policy.