In this work, a relay-selection scheme is proposed for underlay cognitive radio networks, with fixed and adaptive relaying power. The relay-selection and power allocation is based on the calculation of the log-likelihood ratio (LLR) value, calculated at each of the relay nodes available in the secondary network. No interference is caused to the primary network, through the satisfaction of a low power constraint. The proposed schemes' performance is measured and compared in terms of the their BER curves. The effect of the interference caused by the primary network is also investigated.