Location awareness allows to define a concurrent transmission region where a primary and a secondary networks can coexist. We investigate the impact of joint rate and power control on the performance of a cognitive radio ad hoc network overlaying a primary system. The proposed strategies adequately adjust the secondary user transmit power to increase the concurrent transmission probability while respecting a given constraint on the achievable primary rate. Two power control strategies are described: Rate-Efficient Power Control to maximize the secondary capacity, and Energy-Efficient Power Control to minimize the secondary energy consumption. Numerical results show that the proposed schemes expand the concurrent transmission region and that it is possible to increase the average rate and save energy.