In solving judgment aggregation problems, groups often face constraints. Many deci-sion problems can be modelled in terms the acceptance or rejection of certain propo-sitions in a language, and constraints as propositions that the decisions should be consistent with. For example, court judgments in breach-of-contract cases should be consistent with the constraint that action and obligation are necessary and su¢ - cient for liability; judgments on how to rank several options in an order of preference with the constraint of transitivity; and judgments on budget items with budgetary constraints. Often more or less demanding constraints on decisions are imaginable. For instance, in preference ranking problems, the transitivity constraint is often con-strasted with the weaker acyclicity constraint. In this paper, we make constraints explicit in judgment aggregation by relativizing the rationality conditions of consis-tency and deductive closure to a constraint set, whose variation yields more or less strong notions of rationality. We review several general results on judgment aggrega-tion in light of such constraints.