After more than a decade of research on deliberative mini-publics, a number of empirical and theoretical challenges persist. This ranges from the well-known psychological critique of excessive cognitive and deliberative demands on citizens, to the popular claim of undesired group dynamics and biased outcomes (e.g., group polarization) to the democratic challenges of decisiveness and legitimacy. In this paper, we propose a number of advanced empirical routes to deal with these challenges. On the one hand, we suggest a batch of methodological tools and research designs to provide for a more in-depth study the process of citizen deliberation, including a dedicated focus on group dynamics and on the links between process and outcomes. On the other hand, we propose novel ways of looking at legitimacy and decisiveness issues, whereby we discuss conjoint and vignette designs that can shed light on the question what citizens want from deliberative mini-publics.