Constraints describe relations that must be maintained, and provide a useful tool for such applications as interactive simulations, algorithm animation, and graphical user interface construction. We describe a major overhaul and extension to the constraint satisfaction mechanism in ThingLab, a constraint-oriented simulation laboratory written in the Smalltalk-80 language. First, a specification is presented of constraint hierarchies. Such hierarchies include both required constraints and default constraints of differing strengths, thus adding considerable expressive power to the system. Second, an algorithm for satisfying constraint hierarchies is described. The new satisfier is substantially faster than the previous version, even though it also includes new functionality.