Generalization and Suppression are two of the most used techniques to achieve k-anonymity. However, the generalization concept is also used in machine learning to obtain domain models useful for the classification task, and the suppression is the way to achieve such generalization. In this paper we want to address the anonymization of data preserving the classification task. What we propose is to use machine learning methods to obtain partial domain theories formed by partial descriptions of classes. Differently than in machine learning, we impose that such descriptions be as specific as possible, i.e., formed by the maximum number of attributes. This is achieved by suppressing some values of some records. In our method, we suppress only a particular value of an attribute in only a subset of records, that is, we use local suppression. This avoids one of the problems of global suppression that is the loss of more information than necessary.