Dummy messages are usually generated for faking in preserving the location privacy of a sink or source against the global eavesdropping in wireless networks. In this paper, we propose a new method in which a certain number of nodes determined by considering the required privacy level are made to transit to the dormant state doing nothing so that the total number of dummy messages is reduced, while the paths from the sink to the sources are ensured. Through simulation we verify the success ratio of path establishments between the sink and a set of sources and the location privacy level of them.