This paper explores the trade-off between cooperation and secrecy in cognitive radio networks. We consider a scenario consisting of a primary and a secondary system. In the simplest case, each system is represented by a pair of transmitter and receiver. We assume a secrecy constraint on the transmission in the sense that the message of the primary transmitter has to be concealed from the secondary receiver. Both situations where the secondary transmitter is aware and unaware of the primary message are investigated and compared. In the first case, the secondary transmitter helps by allocating power for jamming, which increases the secrecy of the first message. In the latter case, it can also act as a relay for the primary message, thus improving the reliability of the primary transmission. Furthermore, we extend our results to the scenario where the secondary system comprises multiple receivers. For each case we present achievable rate regions. We then provide numerical illustrations for these rate regions. Our main result is that, in spite of the secrecy constraint, cooperation is beneficial in terms of the achievable rates. In particular, the secondary system can achieve a significant rate without decreasing the primary rate below the benchmark rate achievable without the help of the secondary transmitter. Finally, we investigate the influence of the distances between users on the system's performance.