Whether constitution-making should be constrained has long been debated, but little is known about whether it is possible. We make several contributions to this question. We start by providing a typology of three types of constraints on constitution-making: Substantive, Procedural, and Institutional. We next develop a positive theory of when these constraints are likely to influence drafters’ behavior. We then use a mixed-methods approach to explore these ideas in the context of Chile’s constitutional reform process. In a survey experiment conducted in Chile before citizens voted on the draft constitution, we find that most respondents supported constraints in the abstract, but that they also supported a popular policy initiative—nationalizing mines—that violated these same constraints. This suggests that popular opinion may not enforce constraints on constitution-making. However, in fieldwork conducted in Chile, we found evidence that Chilean political parties did rein in constitution-makers who wanted to ignore constraints. This suggests that constitution-making constraints may be more likely to be effective when enforced by political parties.