Effective climate mitigation requires international cooperation, and these global efforts need broad public support to be sustainable over the long run. We provide estimates of public support for different types of climate agreements in France, Germany, the United Kingdom, and the United States. Using data from a large-scale experimental survey, we explore how three key dimensions of global climate cooperation--costs and distribution, participation, and enforcement--affect individuals' willingness to support these international efforts. We find that design features have significant effects on public support. Specifically, our results indicate that support is higher for global climate agreements that involve lower costs, distribute costs according to prominent fairness principles, encompass more countries, and include a small sanction if a country fails to meet its emissions reduction targets. In contrast to well-documented baseline differences in public support for climate mitigation efforts, opinion responds similarly to changes in climate policy design in all four countries. We also find that the effects of institutional design features can bring about decisive changes in the level of public support for a global climate agreement. Moreover, the results appear consistent with the view that the sensitivity of public support to design features reflects underlying norms of reciprocity and individuals' beliefs about the potential effectiveness of specific agreements.