In many experiments where radiation emitted from the surface or lower atmosphere is to be measured, a fundamental difficulty is the presence of clouds. In this paper a technique is developed and described which uses a number of small fields-of-view to estimate the clear radiance. Specifically, it is assumed that some of these small fields-of-view are cloud-free and that the difference between the measured radiance from these cloud-free areas is due to instrument noise, which is normal with known standard deviation. Then the tail of the normal distribution is used to estimate the clear radiance. An example is provided.