In this paper, we address a power allocation problem in a relay-aided cognitive network. The network is composed by a primary and secondary user/ destination pair and a relay, which helps the communication between the secondary user and its destination. The transmission of the secondary user and the helping relay is allowed provided that a minimum quality of service (QoS) constraint is met at the primary user. First, we derive the achievable rate regions under Decode-and-Forward (DF) and Compress-and-Forward (CF) relaying schemes. Then, we provide analytic expressions of the optimal power allocation policies at the secondary user and the relay. Remarkably, if the secondary direct link is negligible -the communication takes place only via the relay - DF is proven to always outperform CF, irrespective from the system parameters. If the secondary direct link is not negligible, our numerical results illustrate that DF outperforms CF only when the relay is close to the secondary user.