This article addresses the question of how the EU exercises power in international politics and, in particular, whether or not there is anything distinctive about the ways in which it does so. Taking a relational approach to power, where the focus is on practical knowledge and perceptions of self and other, the paper departs from the assumption that such a question has to be evaluated in specific settings. Extrapolating from the EU's attempt to influence outcomes in Tunisia and Morocco following the Arab Spring, this paper proposes that the power of ambiguity captures some of the distinctiveness of the EU as a global actor. The paper highlights the ambiguity of what the EU is in the eyes of others, which opens up avenues for exercising power that others lack, not necessarily in accordance with a well-defined agenda, but understood as the production of effects in delimited settings.