In the current pandemic, both self-regulated health-protective behavior and government-imposed regulations are needed for successful outbreak mitigation. Going forward, researchers and decision-makers must therefore understand the factors contributing to individuals’ engagement in health-protective behavior, and their support for government regulations. Integrating knowledge from the literatures on self-control and cooperation, we explore an informed selection of potential predictors of individuals’ health-protective behaviors as well as their support for government regulations during the COVID-19 pandemic. Aiming for a conceptual replication in two European countries, we collected data in Switzerland (N = 352) and the UK before (N = 212) and during lockdown (n = 132) and conducted supervised machine learning for variable selection, followed by OLS regression, cross-sectionally and, in the UK sample, across time. Results showed that personal importance of outbreak mitigation and beliefs surrounding others’ cooperation are associated with both health-protective behavior and support for government regulations. Further, Swiss participants high in trait self-control engaged in health-protective behavior more often. Interestingly, perceived risk, age, and political orientation consistently displayed nonsignificant weak to zero associations with both health-protective behavior and support. Together, these findings highlight the contribution of self-control theories in explaining COVID-19-relevant outcomes, and underscore the importance of contextualizing self-control within the cooperative social context.