A promising technology that tackles the conflict between spectrum scarcity and underutilization is cognitive radio (CR), of which spectrum sensing is one of the most important functionalities. The use of dedicated sensors is an emerging service for spectrum sensing, where multiple sensors perform cooperative spectrum sensing. However, due to the energy constraint of battery-powered sensors, energy efficiency arises as a critical issue in sensor-aided CR networks. An optimal scheduling of each sensor active time can effectively extend the network lifetime. In this paper, we divide the sensors into a number of nondisjoint feasible subsets such that only one subset of sensors is turned on at a period of time while guaranteeing that the necessary detection and false alarm thresholds are satisfied. Each subset is activated successively, and nonactivated sensors are put in a low-energy sleep mode to extend the network lifetime. We formulate such problem of energy-efficient cooperative spectrum sensing in sensor-aided CR networks as a scheduling problem, which is proved to be ${\cal N}{\cal P}$-complete. We employ Greedy Degradation to degrade it into a linear integer programming problem and propose three approaches, namely, Implicit Enumeration (IE), General Greedy (GG), and $\lambda$-Greedy $(\lambda{\rm G})$, to solve the subproblem. Among them, IE can achieve an optimal solution with the highest computational complexity, whereas GG can provide a solution with the lowest complexity but much poorer performance. To achieve a better tradeoff in terms of network lifetime and computational complexity, a brand new $\lambda{\rm G}$ is proposed to approach IE with the complexity comparable with GG. Simulation results are presented to verify the performance of our approaches, as well as to study the effect of adjustable parameters on the performance.