The Orbiting Carbon Observatories-2 and 3 make space-based measurements in the oxygen A-band and the weak and strong carbon dioxide (CO2) bands. A Bayesian optimal estimation approach is employed to retrieve the column averaged CO2 dry air mole fraction from these measurements. This retrieval requires a large number of polarized, multiple-scattering radiative transfer (RT) calculations for each iteration. These RT calculations take up the majority of the processing time for each retrieval, and slow down the algorithm to the point that reprocessing data from the mission over multiple years becomes very expensive. To accelerate the RT calculations and thereby ease this bottleneck, we have developed a novel approach that enables reproduction of the spectra for the three OCO-2/3 instrument bands from radiances calculated at a small subset of monochromatic wavelengths. This allows reduction of the number of monochromatic RT calculations by a factor of 20 and can be achieved with radiance errors of less than 0.1% with respect to the existing algorithm. The technique is applicable to similar retrieval algorithms for other greenhouse gas sensors with large data volumes, such as GeoCarb, GOSAT-3, and CO2M.