Distributed power control is investigated for cognitive radio networks (CRNs) based on a cooperative game-theoretic framework. Taking into consideration both network efficiency and user fairness, a cooperative Nash bargaining power-control game (NBPCG) model is formulated, where interference power constraints (IPCs) are imposed to protect the primary users' (PUs') transmissions, and minimum signal-to-interference-plus-noise ratio (SINR) requirements are employed to provide reliable transmission opportunities to secondary cognitive users. An SINR-based utility function is designed for this game model, which not only reflects the spectrum efficiency of the CRN but also complies with all the axioms in the Nash theorem and, hence, facilitates efficient algorithmic development. The existence, uniqueness, and fairness of this game solution are proved analytically. To deal with the IPCs where the power-control decisions of all users are coupled, these IPCs are properly transformed into a pricing function in the objective utility. Accordingly, a Kalai-Smorodinsky (KS) bargaining solution and a Nash bargaining solution (NBS) are developed, which result in Pareto-optimal solutions to the NBPCG problem with different user-fairness policies. Theoretical analysis and simulations are provided to testify the effectiveness of the proposed cooperative game algorithms for efficient and fair power control in CRNs.