For absorbing wavelengths, we discuss the effect of horizontal solar radiative fluxes in clouds on the accuracy of a conventional plane-parallel radiative transfer calculation for a single pixel, known as the Independent Pixel Approximation (IPA). Vertically integrated horizontal fluxes can be represented as a sum of three components: the IPA accuracies for reflectance, transmittance and absorptance. We show that IPA accuracy for reflectance always improves with more absorption, while the IPA accuracy for transmittance is less sensitive to the changes in absorption: with respect to the non-absorbing case, it may first deteriorate for weak absorption and then improve again for strongly absorbing wavelengths. IPA accuracy for absorptance always deteriorates with more absorption. ¿ 1999 American Geophysical Union