As representative democracy is increasingly criticized, a new institution is becoming popular among academics and practitioners: deliberative citizens’ assemblies. To evaluate whether these assemblies can deliver their promise of re-engaging the dissatisfied with representative politics, we explore who supports them and why. We build on a unique survey conducted with representative samples of 15 Western European countries and find, first, that the most supportive are those who are less educated and have a low sense of political competence and an anti-elite sentiment. Thus, support does come from the dissatisfied. Second, we find that this support is for a part ‘outcome contingent’, in the sense that it changes with respondents’ expectations regarding the policy outcome from deliberative citizens’ assemblies. This second finding nuances the first one and suggests that while deliberative citizens’ assemblies convey some hope to re-engage disengaged citizens, this is conditioned on the expectation of a favourable outcome.