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Publishing data for analysis from a microdata table containing sensitive attributes, while maintaining individual privacy, is a problem of increasing significance today. The k-anonymity model was proposed for privacy preserving data publication. While focusing on identity disclosure, k-anonymity model fails to protect attribute disclosure to some extent. Many efforts are made to enhance the k-anonymity model recently. In this paper, we propose a new privacy protection model called (p+, alpha)-sensitive k-anonymity, where sensitive attributes are first partitioned into categories by their sensitivity, and then the categories that sensitive attributes belong to are published. Different from previous enhanced k-anonymity models, this model allows us to release a lot more information without compromising privacy. We also provide testing and heuristic generating algorithms. Experimental results show that our introduced model could significantly reduce the privacy breach.