Advances in Boolean satisfiability solvers have popularized their use in many of today?s CAD VLSI challenges. Existing satisfiability solvers operate on a circuit representation that does not capture all of the structural circuit characteristics and properties. This work proposes algorithms that take into account the circuit don?t care conditions thus enhancing the performance of these tools. Don?t care sets are addressed in this work both statically and dynamically to reduce the search space and guide the decision making process. Experiments demonstrate performance gains.