Citizens' conferences attempt to include citizens in the decisional and political process. Created to foster deliberation and public debate on disputed issues, they place ordinary citizens in the spotlight and ask them to express their views, after having debated the issues with specialists. Whereas the conferences conducted in a domestic context have been well analyzed, little attention has been given so far to the first attempts to replicate the experience at the European level, and to the specific problems that may be encountered in so doing. Two main reasons have prompted the EU to pay interest to this participatory mechanism: functional reasons (the need to take position on a socio-technological controversy whose stakes are controversial) and political legitimacy (the absence of a strong democratic legitimacy at the EU level). Based on an analysis of the first two experiments organized in the EU, devoted to "the city of tomorrow" and to brain sciences respectively, this article argues that achieving such citizen deliberation is not without problems. In many respects, these problems point to the difficulty entailed in the creation of a European public space: the elusive quest for a "European people"; the question of representation according to the size of the countries; the issue of languages. At the same time, the main potential of this instrument may lie in its cognitive impact, since the interpretations and knowledge surrounding the issues which are debate may influence both the agenda-setting and the decision-making process.