An increasing amount of mobility data is being collected every day by different means, e.g., by mobile phone operators. This data is sometimes published after the application of simple anonymization techniques, which might lead to severe privacy threats. We propose in this paper a new solution whose novelty is twofold. Firstly, we introduce an algorithm designed to hide places where a user stops during her journey (namely points of interest), by enforcing a constant speed along her trajectory. Secondly, we leverage places where users meet to take a chance to swap their trajectories and therefore confuse an attacker.