Spectrum sensing is an important aspect of cognitive radio networks (CRNs). Secondary users (SUs) should periodically sense the channels to ensure primary-user (PU) protection. Sensing with cooperation among several SUs is more robust and less error prone. However, cooperation also increases the energy spent for sensing. Considering the periodic nature of sensing, even a small amount of savings in each sensing period leads to considerable improvement in the long run. In this paper, we consider the problem of energy-efficient (EE) spectrum sensing scheduling with satisfactory PU protection. Our model exploits the diversity of SUs in their received signal-to-noise ratio (SNR) of the primary signal to determine the sensing duration for each user/channel pair for higher energy efficiency. We model the given problem as an optimization problem with two different objectives. The first objective is to minimize the energy consumption, and the second objective is to minimize the spectrum sensing duration to maximize the remaining time for data transmission. We solve both problems using the outer linearization method. In addition, we present two suboptimal but efficient heuristic methods. We provide an extensive performance analysis of our proposed methods under various numbers of SUs, average channel SNR, and channel sampling frequency. Our analysis reveals that all proposals with an energy minimization perspective provide significant energy savings compared with a pure transmission-time maximization (TXT) technique.