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Several methods have been proposed to support location-based services without revealing mobile users' privacy information. There are two types of privacy concerns in location-based services: location privacy and query privacy. Existing work, based on location k-anonymity, mainly focused on location privacy and are insufficient to protect query privacy. In particular, due to lack of semantics, location k-anonymity suffers from query homogeneity attack. In this paper, we introduce p-sensitivity, a novel privacy-protection model that considers query diversity and semantic information in anonymizing user locations. We propose a PE-tree for implementing the p-sensitivity model. Search algorithms and heuristics are developed to efficiently find the optimal p-sensitivity anonymization in the tree. Preliminary experiments show that p-sensitivity provides high-quality services without compromising users' query privacy.