We extend several encoding and decoding techniques from cooperative communications framework, to a cognitive radio system consisting of a primary user (PU) and a secondary user (SU), sending their messages to a common receiver. Assuming that the transmitters and the receiver have full channel state information (CSI) collected and distributed by the common receiver, and that the SU knows the PU's codebook, the cooperation is obtained by block Markov superposition coding, and backwards decoding, which yield a causal overlay scenario. We formulate two rate optimization problems with the aim of, (i) maximizing the sum rate of the system, and (ii) maximizing the rate of the secondary user. We obtain the optimal power allocations for both cases, and the resulting rate regions. The power controlled cooperation turns out to be especially useful when maximizing the sum rate of the system, as it gives the PU significant rate rewards for allowing the cognitive transmitter to access its resources.