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Pointer variables have long been considered useful for constructing and manipulating data structures in traditional programming languages. This article discusses how pointer variables can be integrated into one-way constraint models and indicates how these constraints can be usefully employed in user interfaces. Pointer variables allow constraints to model a wide array of dynamic application behavior, simplify the implementation of structured objects and demonstrational systems, and improve the storage and efficiency of constraint-based applications. This article presents two incremental algorithms—one lazy and one eager— for solving constraints with pointer variables. Both algorithms are capable of handling (1) arbitrary systems of one-way constraints, including constraints that involve cycles, and (2) editing models that allow multiple changes between calls to the constraint solver. These algorithms are fault tolerant in that they can handle and recover gracefully from formulas that crash due to programmer error. Constraints that use pointer variables have been implemented in a comprehensive user interface toolkit, Garnet, and our experience with applications written in Garnet have proven the usefulness of pointer variable constraints. Many large-scale applications have been implemented using these constraints.