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This paper investigates the problem of providing network coverage using wireless sensors that operate on low duty cycles (measured by the percentage time a sensor is on or active), i.e., each sensor alternates between active and sleep states to conserve energy with an average sleep period (much) longer than the active period. The dynamic change in topology as a result of such duty-cycling has potentially disruptive effect on the operation and performance of the network. This is compensated by adding redundancy in the sensor deployment. In this paper we examine the fundamental relationship between the reduction in sensor duty cycle and the required level of redundancy for a fixed performance measure, and explore the design of good sensor sleep schedules. In particular, we consider two types of mechanisms, the random sleep type where each sensor keeps an active-sleep schedule independent of another, and the coordinated sleep type where sensors coordinate with each other in reaching an active-sleep schedule. Both types are studied within the context of providing network coverage. We present specific scheduling algorithms within each type, and illustrate their coverage and duty cycle properties via both analysis and simulation. We show with either type of sleep schedule the benefit of added redundancy saturates at some point in that the reduction in duty cycles starts to diminish beyond a certain threshold in deployment redundancy. We also show that at the expense of extra control overhead, a coordinated sleep schedule is more robust and can achieve higher duty cycle reduction with the same amount of redundancy compared to a random sleep schedule.