A One Health approach holds great promise for attenuating the risk and burdens of emerging infectious diseases (EIDs) in both human and animal populations. Because the course and costs of EID outbreaks are difficult to predict, One Health policies must deal with scientific uncertainty, whilst addressing the political, economic and ethical dimensions of communication and intervention strategies. Drawing on the outcomes of parallel Delphi surveys conducted with policymakers in Singapore and Australia, we explore the normative dimensions of two different precautionary approaches to EID decision-making—which we call regimes of risk management and organizing uncertainty, respectively. The imperative to act cautiously can be seen as either an epistemic rule or as a decision rule, which has implications for how EID uncertainty is managed. The normative features of each regime, and their implications for One Health approaches to infectious disease risks and outbreaks, are described. As One Health attempts to move upstream to prevent rather than react to emergence of EIDs in humans, we show how the approaches to uncertainty, taken by experts and decision-makers, and their choices about the content and quality of evidence, have implications for who pays the price of precaution, and, thereby, social and global justice.