There is now wide agreement that under the pressure of the 2008 crisis serious flaws have emerged in the design of the European Economic and Monetary Union (EMU) as a supranational architecture with the overarching end to generate and distribute collective benefits from integration and "internalisation of externalities" among highly interdependent countries. Consequently, reforms are invoked ideally aimed at fostering further integration among member countries. If we agree that more Europe is needed, we cannot beg the far more controversial question: "Which Europe?" To this end, we introduce a policy game setup of two interdependent countries with reciprocal negative externalities where each sovereign government seeks to optimise its own welfare function reflecting social preferences over policy options and their outcomes. We first establish the welfare losses associated with noncooperative (Nash) policy choices. Then we examine what kind of supranational policy regimes (SRs) may be subscribed to by both governments according to the Pareto criterion. Two SRs are "technocratic" (they do not take national preferences into account), two are "political" (they do). One such regime that we call "Europe" optimises the additive welfare function of the two countries. The thrust of our analysis is that the technocratic regimes are dominated, so that the single alternative is between Europe and "exit" for non-cooperation. Therefore, our analysis lends support to the view that the strategy of further integration by means of an extended system of binding rules enforced by technocratic agencies may be unsuccessful. Yet an important point is that Europe is the Pareto-dominant regime only within a limited range of asymmetry between countries' social preferences.