Abstract The article investigates the institutional and policy choices regarding the EU's relations with the countries and regions covered by the European Neighbourhood Policy (ENP). It juxtaposes the notion of special relationship inaugurated by the Lisbon Treaty to three models for organizing relations with proximate countries: pre-accession, the European Economic Area (EEA) and association. The convergence-access paradigm is found to be the basic pillar of the EU approach. The article brings in a series of dilemmas concerning the design and the implementation of the ENP as well as perceptions from selected partner countries. As a potential way to manage tensions and dilemmas inherent in the EU strategy, the article proposes an altogether novel dimension: decentred integration geared towards polity-building that could partially delink convergence and access. The last section maps out four scenarios for the future directions of the ENP that cover the whole continuum from piecemeal enhancement of the policy to the creation of a European Partnership Area underpinned by a new tier of institutions.