Wireless sensor networks have recently posed many new system building challenges. One of the main problems is energy conservation since most of the sensors are devices with limited battery life and it is infeasible to replenish energy via replacing batteries. An effective approach for energy conservation is scheduling sleep intervals for some sensors, while the remaining sensors stay active providing continuous service. In this paper we consider the problem of selecting a set of active sensors of minimum cardinality that maintains sensing coverage and network connectivity. We study different variations of this problem. The main contribution of this paper is a thorough investigation of algorithms for covering an area with sensors that have fixed locations