Binary Decision Diagrams have been widely used to solve the Boolean Satisfiability (SAT) problem. The individual constraints can be represented using BDDs and the conjunction of all constraints provides all satisfying solutions. However, BDD-related SAT techniques suffer from size explosion problems.This paper presents two BDD-based algorithms to solve the SAT problem that attempt to contain the growth of BDD-size while identifying solutions quickly. The first algorithm, called BSAT, is a recursive, backtracking algorithm that uses an exhaustive search to find a SAT solution. The well known unate recursive paradigm is exploited to solve the SAT problem. The second algorithm, called INCOMPLETE-SEARCH-USAT (abbreviated IS-USAT), incorporates an incomplete search to find a solution. The search is incomplete inasmuch as it is restricted to only those regions that have a high likelihood of containing the solution, discarding the rest. Using our techniques we were able to find SAT solutions not only for all MCNC & ISCAS benchmarks, but also for a variety of industry standard designs.