One of the most important design objectives in wireless sensor networks (WSN) is minimizing the energy consumption since these networks are expected to operate in harsh conditions where the recharging of batteries is impractical, if not impossible. The sleep scheduling mechanism allows sensors to sleep intermittently in order to reduce energy consumption and extend network lifetime. In applications where 100% coverage of the network field is not crucial, allowing the coverage to drop below full coverage while keeping above a predetermined threshold, i.e., partial coverage, can further increase the networklifetime. In this paper, we develop the distributed adaptivesleep scheduling algorithm (DASSA) for WSNs with partial coverage. DASSA does not require locationinformation of sensors while maintaining connectivity andsatisfying a user defined coverage target. In DASSA, nodesuse the residual energy levels and feedback from the sinkfor scheduling the activity of their neighbors. This feedbackmechanism reduces the randomness in scheduling thatwould otherwise occur due to the absence of locationinformation. The performance of DASSA is compared withan integer linear programming (ILP) based centralizedsleep scheduling algorithm (CSSA), which is devised tofind the maximum number of rounds the network cansurvive assuming that the location information of all sensorsis available. DASSA is also compared with thedecentralized DGT algorithm. DASSA attains networklifetimes up to 92% of the centralized solution and it achieves significantly longer lifetimes compared with the DGT algorithm.