In this correspondence, transmit precoders and their power allocation coefficients are designed jointly for a downlink non-orthogonal multiple access (NOMA) wireless communication system. The objective is to provide max-min fairness (MMF) among the strongest users in each group, while maintaining minimum target rates for all the other users. The proposed solutions are respectively based on semi-definite relaxation (SDR) and successive convex approximation (SCA) and on the minimum mean square error (MMSE) approaches. For the latter approach, a simplification is also suggested to lower complexity. It is shown that while rate-splitting (RS) has the best MMF rates, the low-complexity MMSE approach has the least complexity. Moreover, the SDR/SCA approach offers an excellent tradeoff between the two.