K-Anonymity technique is a useful way to protect privacy in information sharing. This paper presents a practical framework for implementing one type of k-anonymization, based on which a greedy algorithm named Nibble for producing approximately minimal generalizations is introduced. Experiments show that Nibble often reflects the multivariate distribution of the microdata more faithfully than the multidimensional partitioning approaches, as measured both by the generally accepted quality metrics and our proposed information loss metric: average number of alternative values.