Wireless sensor networks have emerged recently as an effective way of monitoring remote or inhospitable physical environments. One of the major challenges in devising such networks lies in the constrained energy and computational resources available to sensor nodes. These constraints must be taken into account at all levels of the system hierarchy. The deployment of sensor nodes is the first step in establishing a sensor network. Since sensor networks contain a large number of sensor nodes, the nodes must be deployed in clusters, where the location of each particular node cannot be fully guaranteed a priori. Therefore, the number of nodes that must be deployed in order to completely cover the whole monitored area is often higher than if a deterministic procedure were used. In networks with stochastically placed nodes, activating only the necessary number of sensor nodes at any particular moment can save energy. We introduce a heuristic that selects mutually exclusive sets of sensor nodes, where the members of each of those sets together completely cover the monitored area. The intervals of activity are the same for all sets, and only one of the sets is active at any time. The experimental results demonstrate that by using only a subset of sensor nodes at each moment, we achieve a significant energy savings while fully preserving coverage.