This article critically examines spectroscopic data for the two lowest states (X (1)Sigma (+) and a (3)Sigma (+)) for NaRb, which dissociate to ground state Na and Rb atoms. A more precise triplet state RKR potential curve is reported. A complete hybrid potential for the triplet state is determined, based on the improved RKR curve plus Coulombic and exchange contributions at long range. A new, more precise dissociation energy for the a (3)Sigma (+) state is determined: D-e = 183.0 +/-0.10 cm(-1). Previously unpublished and improved Dunham coefficients for the singlet state are reported, which cover the bottom 57% of the well. A complete hybrid potential energy curve for the singlet state is determined, based on the RKR curve plus Coulombic and exchange contributions at long range. The X (1)Sigma (+) state potential curve now covers 100% of the well and a new, precise dissociation energy is determined: D-e=5030.75 +/-0.10 cm(-1). Three additional unobserved energy levels are predicted for the a (3)Sigma (+) state of (NaRb)-Na-23-Rb-85, all within 1.1 cm(-1) of the dissociation limit.