Data publishing generates much concern over the protection of individual privacy. In the well-known kanonymity model and the related models such as l-diversity and (α, k)-anonymity, the adversary is assumed to possess knowledge about an external table with information of the quasi-identifiers of individuals. In this paper, we show that knowledge of the mechanism or algorithm of anonymization for data publication can also lead to extra information that assists the adversary and jeopardizes individual privacy. In particular, all known mechanisms try to minimize information loss and such an attempt provides for a loophole for attacks. We call such an attack a minimality attack. In this paper, we propose a model called mconfidentiality which deals with the individual privacy issue with the consideration of minimality attacks. Though the problem of optimal m-confidentiality anonymization is NP-hard, we propose an algorithm which generates m-confidential data sets efficiently. We also ...