The European Parliament under the currentcooperation procedurehas an important power: it can make proposals that, if accepted by the Commission of the European Communities, are easier for the Council of Ministers to accept than to modify, since only qualified majority is required for acceptance, whereas full unanimity for modification. The importance of this power, which I call the power of theconditional agenda setter, has not been recognized in previous scholarly work. For structural reasons explained in the text, this power is likely to increase in the future. I conclude by arguing that the conditional delegation of power to international actors (the European Parliament, Commission, and the Court of Justice) is a frequent phenomenon in European institutions. This delegation presents three important advantages: it makes possible the selection of one among many possible equilibria, it accelerates European integration, and it diffuses responsibility for politically unpopular measures.