Most previous research on privacy-preserving data publishing, based on the k-anonymity model, has followed the simplistic approach of homogeneously giving the same generalized value in all quasi-identifiers within a partition. We observe that the anonymization error can be reduced if we follow a non-homogeneous generalization approach for groups of size larger than k. Such an approach would allow tuples within a partition to take different generalized quasi-identifier values. Anonymization following this model is not trivial, as its direct application can easily violate kanonymity. In addition, non-homogeneous generalization allows for additional types of attack, which should be considered in the process. We provide a methodology for verifying whether a nonhomogeneous generalization violates k-anonymity. Then, we propose a technique that generates a non-homogeneous generalization for a partition and show that its result satisfies k-anonymity, however by straightforwardly applying it, ...