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We present an algorithm for simplifying the solution of conjunctive Boolean constraints of state and input variables, in the context of constrained random vector generation using BDDs. The basis of our approach is the extraction of "hold-constraints" from the constraint system. Hold-constraints are deterministic and trivially resolvable; in addition, they can be used to simplify the original constraints as well as refine the conjunctive partition. Experiments demonstrate significant reduction in the time and space needed for constructing the conjunction BDDs, and the time spent in vector generation during simulation.