In this paper we study the computation of the Nash bargaining solution for the two players, K frequency bands case, under joint FDM/TDM spectrum allocations and total power constraint. The results improve previous analysis by Han et al. We provide a computationally efficient algorithm as well as detailed analysis of the Karush-Kuhn-Tucker (KKT) equations necessary for proving the correctness of the algorithm. Simulation results demonstrating the gain of the NBS over competitive approaches are also provided.