Deliberative mini-publics convene a panel of randomly selected constituents to deeply engage with complex policy issues. This essay considers the process of selecting the members of this panel, with a particular focus on the central role of randomness in this process. Among other benefits, this random- ness confers legitimacy by affording all members of society some chance of participation. The main constraint placed on this selection process is representativeness—the requirement that the resulting panel accurately reflects the demographic and ideological makeup of the population. Within this constraint, there is a vast space of possible ways to randomly choose a panel, and each method spreads the random chance of selection differently across willing participants. In this essay, we explore approaches for inten- tionally designing this randomness to promote specific goals, such as increasing fairness, transparency, non-manipulability, and richness of representation in mini-publics.