There is a solid theoretical literature that discusses both the democratic credentials and the shortcomings of the use of random selection as a mechanism to shape political bodies. Many institutional innovations, from deliberative polls to citizens' assemblies, are currently being implemented around the world. However, both the literature and the new institutional designs usually refer to the legislative and executive branches of government. Academics rarely discuss novel uses of the lottery in the judicial branch, particularly in constitutional aspects. In this paper, I consider whether it would be appropriate to use the draw in specific constitutional domains. I discuss, among other alternatives, the use of a lottery to select judges and cases, the use of deliberative polls by courts, the articulation of mini publics with judicial instances, and the combination of elected and randomly selected political bodies to amend constitutions.