Radiances measured at two different wavelengths or angles, with a resulting difference in absorption, can be used to determine the atmospheric attenuation of the surface radiance so that sea surface temperatures can be derived. Previous investigations used a correction equal to a constant times the difference in measured radiances. Some of these investigations were based on radiances calculated from models that underestimated absorption in moist atmospheres. When better transmittance models were used, the accuracy decreased. Radiances at 835 cm-1 are calculated for moist atmospheres at different zenith angles to test methods used to correct infrared measurements for atmospheric attenuation. Higher-order corrections are compared to first-order corrections and are shown to result in a significant increase in accuracy, reducing the rms error by one third, from 0.6 K to 0.4 K.