Without consideration of the minimum signal-to-interference-plus-noise ratio (SINR) and frequent information exchange, traditional power control algorithms can not always satisfy SINR requirements of secondary users (SUs) and primary users (PUs) in cognitive radio networks. In this paper, a distributed power control problem for maximizing total throughput of SUs is studied subject to the SINR constraints of SUs and the interference constraints of PUs. To reduce message exchange among SUs, two improved methods are obtained by dual decomposition approaches. For a large-scale network, an average interference constraint is presented at the cost of performance degradation. For a small-scale network, a weighted interference constraint with fairness consideration is proposed to obtain good performance. Simulation results demonstrate that the proposed algorithm is superior to ADCPC and TPCG algorithms.