Several static analysis techniques, e.g., symbolic execution or scope-bounded checking, as well as dynamic analysis techniques, e.g., specification-based testing, use constraint solvers as an enabling technology. To analyze code that manipulates structurally complex data, the underlying solver must support structural constraints. Solving such constraints can be expensive due to the large number of aliasing possibilities that the solver must consider. This paper presents a novel technique to selectively reduce the number of test cases to be generated. Our technique applies across a class of structural constraint solvers. Experimental results show that the technique enables an order of magnitude reduction in the number of test cases to be considered.