k-anonymity is a popular measure of privacy for data publishing: It measures the risk of identity-disclosure of individuals whose personal information are released in the form of published data for statistical analysis and data mining purposes(e.g. census data). Higher values of k denote higher level of privacy (smaller risk of disclosure). Existing techniques to achieve k-anonymity use a variety of “generalization” and “suppression” of cell values for multi-attribute data. At the same time, the released data needs to be as “information-rich” as possible to maximize its utility. Information loss becomes an even greater concern as more stringent privacy constraints are imposed . The resulting optimization problems have proven to be computationally intensive for data sets with large attribute-domains. In this paper, we develop a systematic enumeration based branchand-bound technique that explores a much richer space of solutions than any previous method in literature. We further enhance the basic algorithm to incorporate heuristics that potentially accelerate the search process significantly.