Privacy concerns place a great impediment to publishing and/or exchanging trajectory data across companies and institutions. This has urged researchers to address privacy issues prior to trajectory data release. Currently, privacy preserving solutions distort original data unnecessarily, hence, degrade data utility and make such data less useful for third parties. We consider a trajectory as a sequence of stops and moves, and propose an approach that exploits features of a trajectory as means for preserving privacy while maintaining a high level of utility. We introduce the concept of sensitivity for stops based on the assumption that they are more vulnerable to privacy threats. We propose an efficient algorithm that either substitutes sensitive stop points of a trajectory with moves from the same trajectory or introduces a minimal detour if a less sensitive stop can not be found on the same route. Our experiments shows that our method balances user privacy and data utility: it protects privacy through preventing an adversary from making inferences about sensitive stops while maintaining a high level of data similarity to the original dataset.