Greater cooperation with third countries is one of the EU's core responses to the refugee crisis. This cooperation is focused on the readmission of individuals irregularly staying in the EU, on border surveillance and control, and on the reception of refugees in third countries. The EU has attempted to co-opt Turkey and African countries into these priorities, using funding and specific mobility channels as incentives. This paper poses the question of what kind of cooperation the EU should pursue with third countries. As the current approaches are not new, we present the lessons from the EU's long cooperation with Morocco to inform the current debate. We find that, first, the difficult negotiations on an EU Readmission Agreement with Morocco show that more funding or 'incentives' cannot guarantee such an agreement, let alone its implementation. Second, we highlight the challenges of the partly EU-funded and Frontex-coordinated cooperation on borders between Spain and Morocco, which hampers the capacity of third countries to respect migrants' rights and challenges the obligations of EU member states under European and international law. Third, as EU cooperation with Turkey and Africa now aims to 'stem' the flow of asylum-seekers, the capacity of third countries to offer reception and protection to asylum-seekers is crucial. We conclude that Morocco has limited capacities in this regard, which raises the question of whether third countries can be assumed to be able to offer such reception and protection.