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Energy-efficient design has become increasingly important to battery-powered wireless devices. In this paper, we focus on the energy efficiency of a cognitive radio network, in which a secondary user senses the channels licensed to some primary users sequentially before it decides to transmit. Energy is consumed in both the channel sensing and transmission processes. The energy-efficient design calls for a careful design in the sensing-access strategies and the sensing order, with the sensing strategy specifying when to stop sensing and start transmission, the access strategy specifying the power level to be used upon transmission, and the sensing order specifying the sequence of channel sensing. Hence, the objective of this paper is to identify the sensing-access strategies and the sensing order that achieve the maximum energy efficiency. We first investigate the design when the channel sensing order is given and formulate the above design problem as a stochastic sequential decision-making problem. To solve it, we study another parametric formulation of the original problem, which rewards transmission throughput and penalizes energy consumption. Dynamic programming can be applied to identify the optimal strategy for the parametric problem. Then, by exploring the relationship between the two formulations and making use of the monotonicity property of the parametric formulation, we develop an algorithm to find the optimal sensing-access strategies for the original problem. Furthermore, we study the joint design of the channel sensing order and the sensing-access strategies. Lastly, the performance of the proposed designs is evaluated through numerical results.