In this paper, we consider a heterogeneous ad-hoc network where primary users may cooperate with cognitive radio (CR) users for the transmission of their data. We propose a new cooperation protocol that allows CR users to relay primary user signals in exchange for some spectrum. The spectrum released by primary users is used by CR users for their own data transmission. The proposed protocol maximizes the primary user power savings and the CR users' own data transmission rate. In addition, it provides more robust (potentially continuous) service for CR users, compared to the conventional practice in cognitive networks where cognitive users transmit in the spectrum holes of primary users (i.e., their service is interrupted when primary users need to transmit and no spectrum holes are available). More specifically, we propose a CR user power allocation scheme that maximizes the rate of transmission of CR user own data, for any given CR user power budget and a given bandwidth released from the primary user. Furthermore, we determine a range of possible transmission power levels that can be used by the primary user during cooperation without sacrificing its target transmission rate, and we derive a necessary condition on the quality of the channel between the primary user and the CR user that enables cooperation. Extensive numerical and simulation studies illustrate our theoretical developments and show that cooperation between a primary and CR user may lead, for example, to up to 80% savings of primary user power when compared to a noncooperation scheme at the same transmission power level.