One critical issue in designing and managing a wireless sensor network is how to save the energy consumption of the sensors in order to maximize network lifetime under the constraint of full coverage of the monitored targets. In this paper, we adopt the common approach of creating disjoint sensor covers to prolong network lifetime. The typical goal used in the literature is to maximize the number of covers without consideration of the energy levels of the sensors. We argue that the network lifetime can be extended by maximizing the total bottleneck energy of the created covers. We formally define the problem of maximizing the total bottleneck energy of the covers, present for the first time an integer programming formulation of the problem, and develop two algorithms to solve large problem instances. Extensive experimental tests show that the use of the goal of maximizing the total bottleneck energy of the covers creates covers with substantially longer network lifetime than the lifetime of the covers created with the goal of maximizing solely the number of covers.