Numerous privacy models based on the k-anonymity property have been introduced in the last few years. While differing in their methods and quality of their results, they all focus first on masking the data, and then protecting the quality of the data as a whole. We consider a new approach, where requirements on the amount of distortion allowed on the initial data are imposed in order to preserve its usefulness. In this paper, the constrained psensitive k-anonymity model is introduced and an algorithm for generating constrained p-sensitive k-anonymous microdata is presented. Our experiments have shown that the proposed algorithm is comparable quality-wise with existing algorithms. Categories and Subject Descriptors K.4.1 [Computers and Society]: Public Policy Issues – privacy. I.5.3 [Pattern Recognition]: Clustering – algorithms. General Terms Algorithms, Security. Keywords P-Sensitive K-Anonymity, Anonymization, User Constraints.