With the current sovereign debt crisis, the incompleteness of economic integration in the Economic and Monetary Union (EMU) has become patent, leading to an intense debate among academics and policy makers. Much of the debate concerns fiscal rules and austerity measures, both of which weigh on growth prospects. In this paper we look at the main structural shortcomings of EMU through the lens of general equilibrium theory. We address two issues (international sharing of macroeconomic risks and coordinated growth stimulation) which are at the heart of the sustainability of EMU. We propose: (A) a specific scheme for mutual insurance of macroeconomic risks; (B) locating responsibility for demand policies at the EMU level, with ambitious investment programs (public, or fiscally-neutral private) as main instrument.