A new very narrow band model (VNBM) approach has been developed and incorporated into the MODTRAN atmospheric transmittance–radiance code. The VNBM includes a computational spectral resolution of 1 cm−1, a single-line Voigt equivalent width formalism that is based on the Rodgers–Williams approximation and accounts for the finite spectral width of the interval, explicit consideration of line tails, a statistical line overlap correction, a new sublayer integration approach that treats the effect of the sublayer temperature gradient on the path radiance, and the Curtis–Godson (CG) approximation for inhomogeneous paths. A modified procedure for determining the line density parameter 1/d is introduced, which reduces its magnitude. This results in a partial correction of the VNBM tendency to overestimate the interval equivalent widths. The standard two parameter CG approximation is used for H2O and CO2, while the Goody three parameter CG approximation is used for O3. Atmospheric flux and cooling rate predictions using a research version of MODTRAN, MODR, are presented for H2O (with and without the continuum), CO2, and O3 for several model atmospheres. The effect of doubling the CO2 concentration is also considered. These calculations are compared to line-by-line (LBL) model calculations using the AER, GLA, GFDL, and GISS codes. The MODR predictions fall within the spread of the LBL results. The effects of decreasing the band model spectral resolution are illustrated using CO2 cooling rate and flux calculations.