© 2015 ACM. Preservation of user privacy is paramount in the publication of datasets that contain fine-grained information about individuals. The problem is especially critical in the case of mobile traffic datasets collected by cellular operators, as they feature high subscriber trajectory uniqueness and they are resistant to anonymization through spatiotemporal generalization. In this work, we first unveil the reasons behind such undesirable features of mobile traffic datasets, by leveraging an original measure of the anonymizability of users’ mobile fingerprints. Building on such findings, we propose GLOVE, an algorithm that grants k-anonymity of trajectories through specialized generalization. We evaluate our methodology on two nationwide mobile traffic datasets, and show that it achieves k-anonymity while preserving a substantial level of accuracy in the data.