We present a simplified version of an average-atom collisional-radiative model employing both local-thermodynamic-equilibrium average-atom and isolated-ion atomic data. The simplifications introduced do not lead to any substantial errors, and they significantly speed up calculations compared with the basic average-atom model involving direct solution of the self-consistent-field equations. Average ion charges, charge state distributions, and emission spectra of non-local-thermodynamic-equilibrium (NLTE) gold plasmas calculated using various modifications of the average-atom collisional-radiative model are compared with those obtained using the THERMOS model with the detailed configuration accounting approach. We also propose an efficient method to calculate thermodynamic functions of NLTE plasmas in the context of the simplified average-atom collisional-radiative model.