A three-parameter scaling approximation is developed in conjunction with random models for the computation of transmittance along nonhomogeneous atmospheres. In addition to the scaled path length and pressure, a third parameter is introduced to account for intermediate absorption. With reference to the results derived from line-by-line calculations, we assess the accuracy of this scaling approximation in different atmospheric conditions. For the O3 9.6-μm band where the Curtis-Godson and other conventional scaling methods usually produce large errors, the present model can achieve relative accuracies within ~1% in transmittance and the downward surface flux. Accuracy of ~0.15 K/d can be obtained in cooling rate calculations. The present three-parameter approximation is well suited for radiative transfer parameterizations in which the demand for high accuracy is required in the transmittance and flux calculations. ¿ American Geophysical Union 1992