There is increasing scientific consensus that a One Health approach (acknowledging links between human, animal and environmental health) is the most effective way of responding to emerging infectious disease (EID) threats. However, reviews of past EID events show that successful implementation of control strategies hinge on alignment with public values. Given the limited evidence about public values in this area, we sought to understand public preferences for attributes associated with One Health strategies for EID prevention and control, using a discrete choice experiment (DCE). The DCE was conducted in 2016 using an online panel of Australian respondents aged over 18. Participants were presented with 18 pairs of scenarios describing One Health strategies and outcomes, and asked to select their preferred one. Scenarios were described by nine attributes with varying levels: personal autonomy, economic development, environmental health, community cohesion, free trade and travel, zoonotic risk, mortality, animal welfare and food security. Respondents were broadly representative of the Australian population (n = 1999, mean age 45.3 years (range 18–89); 50.7% male). The public preferred scenarios in which individual freedoms are not restricted for the greater good; unemployment is low; the environment is healthy; there is good community cohesion; travel, imports and exports are tightly controlled; there is lower mortality and incidence of disease; and where animal welfare and food security are protected. Although lower morbidity and mortality were preferable, respondents were willing to accept extra cases of severe disease and deaths to avoid reductions in some attributes. However, a mixed logit model indicated significant heterogeneity. A latent class analysis suggested wide variability across respondent classes in the valuation of attributes, and the trade-offs respondents were willing to accept. Therefore, a single approach to managing EID using One Health is unlikely to be acceptable to all community members.