A detailed description is given of the direct computation of atmospheric transmittance and clear column radiances for the channels of HIRS2 and MSU as a function of atmospheric and surface conditions. Observations are compared with calculated radiances derived from colocated oceanic radiosondes. Under clear conditions, calculated brightness temperatures for the HIRS2 channels have a standard deviation of the order of 0.7¿C compared with observations, while MSU channels have a standard deviation of about 1¿C. Small biases are found in some channels that can be removed by an empirical 'tuning' with coefficients that can be successfully transfered from one season to anothe. Comparison of calculations with 'reconstructed' clear radiances, which are used in analysis of sounding data under partially cloudy conditions, show slightly poorer agreement. The radiance calculation, when used in a temperature retrieval algorithm based on finding solutions to the radiative transfer equations, is shown to be accurate enough to allow for significant improvement of a poor initial on the one hand and only moderate degradation of a perfect initial guess on the other. A rapid transmittance algorithm giving atmospheric transmittance as a function of temperature profile, water vapor profile, ozone profile, and zenith angle of observation is described in the appendix and is shown to introduce insignificant errors in the radiative transfer calculations.