In this paper we study cognitive radio networks with secrecy constraints on the primary transmission. In particular we consider several transmission schemes for the secondary transmitter, namely interference neutralization (IN) and cooperative jamming with and without clean relaying (CR). We derive and analyze the achievable secondary rate performance of the schemes. Furthermore we thoroughly investigate the advantages and shortcomings of these schemes through numerical simulations in a geometric model where we highlight the impact of the users' locations and show the important difference in all schemes depending on the topology. Our results show that the secondary transmitter can successfully adapt its transmission scheme (and parameters), i.e., either IN or CR, depending on its location to maximize its rate while insuring perfect secrecy of the primary transmission.