Privacy preservation is an important issue in the release of data for mining purposes. Recently, a novel l-diversity privacy model was proposed, however, even an l-diverse data set may have some severe problems leading to reveal individual sensitive information. In this paper, we remedy the problem by introducing distinct (l, α)-diversity, which, intuitively, demands that the total weight of the sensitive values in a given QI-group is at least α, where the weight is controlled by a pre-defined recursive metric system. We provide a thorough analysis of the distinct (l, α)-diversity and prove that the optimal distinct (l, α)-diversity problem with its two variants entropy (l, α)-diversity and recursive (c, l, α)-diversity are NP-hard, and propose a top-down anonymization approach to solve the distinct (l, α)-diversity problem with its variants. We show in the extensive experimental evaluations that the proposed methods are practical in terms of utility measurements and can be implemented efficiently.