What is the relative power of the European Commission, the Council of Ministers and the European Parliament (EP) in the European Union (EU)? Both scholars and practitioners of EU affairs provide different answers to this seemingly straightforward question. In this article, we examine the balance of power among these three actors in the context of legislative decision-making. We report the results of a small survey among a select group of practitioners of EU affairs. Their judgements on the relative power of the three organizations vary considerably. We distinguish between two contrasting views: a Council-centric view that attributes more power to the Council of Ministers than to the Commission and Parliament, and a supranational view that attributes large amounts of power to the supranational organizations relative to the Council. To test the veracity of these alternative views, we incorporate them into two variants of a simple and testable bargaining model that makes forecasts of decision outcomes, based on information on actors' preferences. The models are then applied to a dataset that includes information on EU actors' policy positions on 162 controversial issues of which the decision outcomes are known. The variant of the bargaining model incorporating the Council-centric view provides significantly more accurate forecasts.