In this paper, we propose an adaptive cooperative diversity scheme with joint multiple-relay selection and power optimization for multiple-relay cognitive radio networks. Our aim is to improve the performance of secondary transmissions while ensuring the quality of service (QoS) of primary transmissions. Proposed method has lower computational cost for multiple relay selection compared to the "best" relay selection approach, and other similar methods in the literature. Moreover, since the relay selection is performed iteratively until a threshold SNR is reached, we are able to optimize the power consumption simultaneously. Hence, we attain an improved system throughput in cognitive radio networks using the least possible number of relays with optimal power distribution.