Existing literature is overwhelmingly sceptical about the capacity of the Council Presidency to shape the EU agenda. The Presidency's ability to promote private concerns is considered highly limited and, typically, the Presidency is depicted as a 'responsabilite' sans pouvior'. This article challenges the conventional wisdom on theoretical and empirical grounds. Theoretically, it develops a conceptual framework that expands the notion of influence, by distinguishing between three forms of agenda-shaping: agenda-setting, agenda-structuring and agenda exclusion. In this exercise, I draw on theories of bargaining and decision-making developed in international relations and American politics. Empirically, the article provides an inventory of the instruments available to the Presidency within each form of agenda-shaping, as well as illustrative cases that demonstrate how Presidencies regularly influence outcomes in EU policy-making. Illustrations are drawn primarily from the six consecutive Presidencies in the period 1999-2001: Germany, Finland, Portugal, France, Sweden and Belgium.