People nowadays rely heavily on technology and prefer being provided with personalized services. Location based services (LBS) are one of those highly popular services. Users provide their location information in some query to the LBS server, which in turn processes the query and returns personalized results. The major concern when dealing with these services is the privacy issue. Mainly, there are two privacy issues, the user’s identity and the user’s location. Not securing such information could result in some threats to the user. To preserve the user’s privacy, researchers have proposed spatial cloaking to blur the user’s location by a trusted location anonymizer server. Existing methods suffer from high communication cost due to the large number of communication rounds between the user’s device and the cloud server to answer the query. In this paper, we propose an efficient k-anonymity algorithm, called Aman, to compute the cloaked area with minimal number of communication rounds between the user and the cloud server. Unlike existing methods in which the server starts the search from the root or the leaves of the indexing structure, Aman algorithm reduces the search time by starting the search at an intermediate estimated level of the indexing structure that is as close as possible to the queried location. To preserve the user’s privacy, Aman uses k-anonymity cloaking to hide the user’s location. The experimental results using synthetic and real datasets show that Aman outperforms other state-of-the-art approaches.