What preferences do people have for cross-country cooperation on irregular migration and refugee protection? While existing research improves our understanding of how voters react to large-scale inflows of asylum seekers, like those experienced by European countries in 2015–2016, and the type of asylum seekers and policies preferred by European citizens, we know less about people's views concerning a particular EU response to the so-called ‘refugee crisis’, namely the cooperation it agreed with Turkey in March 2016 to stem inflows of asylum seekers and other migrants. To study such views, we build on several strands of the international relations literature exploring key determinants of public preferences for international cooperation on cross-national issues, namely (a) sociotropic concerns, (b) humanitarian considerations, and (c) perceptions of fairness and reciprocity. Our research design leverages conjoint experiments conducted simultaneously in Germany, Greece, and Turkey. We find that the three factors play indeed a role in explaining preferences in the three countries. Moreover, while respondents are favorable to several core features of the current EU-Turkey migration deal (regarding the return of irregular migrants, financial aid to refugees, and border controls), we also find evidence of public support for increased cooperation on resettlement and EU support to Greece to deal with migration, which goes beyond the status quo. In certain aspects of cooperation, public preferences seem to respond to interactions between policy dimensions that capture reciprocity. These findings have important implications for research on public preferences for asylum and migration policies and public support for international cooperation more generally.