Accurate atomic models for astrophysical plasma can be very complex, requiring thousands of states. However, for a variety of applications such as large-scale forward models of the Stokes parameters of a spectral line in the solar corona, it is necessary to build much reduced atomic models. We present two examples of such models, focused on the two near-infrared Fe XIII lines observed on the ground at 10 750 and 10 801 Å. These lines are primary diagnostics for a range of missions (especially the Daniel K. Inouye Solar Telescope, DKIST) to measure electron densities and magnetic fields in the solar corona. We calculate the Stokes parameters for a range of coronal conditions using CHIANTI (for intensities) and P-CORONA (for intensities and polarization), and use P-CORONA and a realistic global magnetohydrodynamic simulation to show that the reduced models provide accurate results, typically to within 5 per cent those obtained with larger models. Reduced models provide a significant decrease (over three orders of magnitude) in the computational time in spectropolarimetric calculations. The methods we describe are general and can be applied to a range of conditions and other ions.