Abstract-Topology control is one of the main techniques that can be used to decrease energy spenditure in wireless sensor networks. Although it has been the subject of much research, less attention has been devoted to study the effects of overhearing on topology control, i.e., the effects of the cost implied by nodes hearing transmissions even if these transmissions were not intended to them. In this paper we describe a distributed (localized) algorithm for topology control in wireless sensor networks. Our approach differs from previous work mainly in the sense that it takes the effects of overhearing into consideration and that it might eliminate more communication links from a given connectivity graph, and thus possibly assign lower transmission power to some nodes. This is done by eliminating so-called k-redundant edges, instead of eliminating only tworedundant edges. We present the sketch of the proof of properties of the algorithm and simulation results.