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This letter investigates the energy-efficient power allocation for orthogonal frequency division multiplexing (OFDM) based cognitive radio networks (CRNs). The problem is to maximize the energy-efficiency measured using the "throughput per Joule" metric subject to the total transmit power and interference constraints. It is then transformed into an equivalent convex problem using parametric programming. Furthermore, an optimal iterative algorithm based on convex optimization theory and parametric programming is proposed. The numerical results show that the proposed optimal algorithm can achieve higher energy-efficiency than that obtained by solving the original problem directly because of its non-convexity. Energy-efficiency maximization can also achieve a good tradeoff between capacity and energy in CRNs.