In this paper, outage performance of cognitive cooperative radio networks using two decode-and-forward (DF) schemes is investigated. Subject to the joint outage constraint of the primary user and the peak transmit power constraint of the secondary user, adaptive power allocation policies for the secondary transmitter and secondary relays are studied. Based on these strategies, expressions for the outage probability of proactive and reactive DF schemes are obtained. Interestingly, our results show that an increase in the transmit power of the primary transmitter (PU-Tx) does not always degrade the performance of the secondary network. In fact, the PU-Tx transmit power is a substantial parameter that the secondary users can adapt to in order to improve the system performance. The numerical results additionally show that the performance of the reactive DF scheme outperforms the proactive DF scheme if the outage threshold in the first hop of the reactive DF scheme is less than that of the proactive scheme.