The technique of k-anonymization allows the releasing of databases that contain personal information while ensuring some degree of individual privacy. Anonymization is usually performed by generalizing database entries. We formally study the concept of generalization, and propose two information-theoretic measures for capturing the amount of information that is lost during the anonymization process. Those measures are more general and more accurate than those proposed in  and . We study the problem of achieving k-anonymity with minimal loss of information. We prove that it is NP-hard and study polynomial approximations for the optimal solution. Our first algorithm gives an approximation guarantee of O(ln k) - an improvement over the best-known O(k)-approximation of . As the running time of the algorithm is O(n 2k), we also show how to adapt the algorithm of  in order to obtain an O(k)-approximation algorithm that is polynomial in both n and k.