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Energy efficient communication is a key requirement of energy-constrained underwater sensor networks (UWSNs). In this paper, we show that the cooperative diversity, which is conventionally utilized to improve reliability in UWSNs, can be employed to reduce energy consumption and preserve a reasonable level of data reliability and communication delay. We first elucidate in what circumstances the cooperative diversity saves energy compared to the non-cooperative diversity. We show that this largely depends on parameters such as distance between the source and the destination node, the location of potential partner node, and the requirements of reliability and communication delay. Second, we propose a simple but effective cooperation scheme to take advantage of the cooperative diversity. The cooperation diversity can achieve a near-optimal energy saving in some circumstances, and it is no worse than the non-cooperative diversity in all cases. Our work provides instructive theoretical guidelines for designing practical UWSNs.