Bounded Model Checking (BMC) is incomplete without a completeness threshold (CT ) bound. Previous methods, using recurrence diameter for obtaining CT , check for existence of a longest loop-free path at every depth k. For terminating software programs, we propose an efficient method for obtaining CT that requires solving a formula of size O(k) at some depths only, as compared to previous methods that require solving a formula of O(k2) (or O(klogk)) size at every depth. We augment previous methods for BMC simplifications using model transformation and control flow information, with context-sensitive analysis. This results in more BMC simplifications and further reduction in the number of CT checks. We have implemented our techniques in a Satisfiability Modulo Theory (SMT)-based BMC framework. Our controlled experiments on real-world software programs show that our proposed formulation provides significant improvements over previous approaches.