The paper takes into account both the concerns of the EU, arguing that convergence is incomplete, and the demands from accession countries, claiming that monetary integration is optimal. Indicators are developed which measure convergence and optimality in comparison with a reference group of the four EMU-member countries Greece, Ireland, Portugal, and Spain. The general conclusion is that the demand of accession countries for entry into EMU can be supported by looking at the net benefits from monetary integration. The more serious problem is a lack of convergence which could imply serious risks during the transition towards monetary union.The paper takes into account both the concerns of the EU, arguing that convergence is incomplete, and the demands from accession countries, claiming that monetary integration is optimal. Indicators are developed which measure convergence and optimality in comparison with a reference group of the four EMU-member countries Greece, Ireland, Portugal, and Spain. The general conclusion is that the demand of accession countries for entry into EMU can be supported by looking at the net benefits from monetary integration. The more serious problem is a lack of convergence which could imply serious risks during the transition towards monetary union.