What preferences do people have for cooperation between high and lower-income countries on irregular migration and refugee protection? Despite the increase in the number and breadth of cross-country cooperation agreements in this policy area, we know little about people’s preferences for such policies. This paper addresses this question in the context of the EU-Turkey ‘migration deal’ agreed in 2016. We conduct cross-country conjoint experiments in Germany, Greece, and Turkey to shed light on the types of policies that generate public support for cross-country cooperation on irregular migration and refugee protection. Our respondents are favorable to several core features of the current EU-Turkey migration deal regarding the return of irregular migrants, financial aid to refugees in Turkey, and the intensity of Turkish border controls. We also find evidence of public support for cooperation on resettlement and EU support to Greece to deal with migration. In certain aspects of cooperation, public preferences seem to respond to interactions between policy dimensions. For example, German public support for relocating refugees from Greece is enhanced if there are stepped-up border controls in Turkey. These findings have important implications for research on public attitudes to asylum and migration policies, ‘migration diplomacy’ in international relations, and public backlash against international cooperation more generally.