When a shade-ring is used to shield a pyranometer from direct solar radiation, a correction to the measured diffuse radiation is necessary to account for diffuse radiation occluded by the ring. The shade-ring correction depends on the dimensions and positioning of the ring and on the anisotropy of sky radiance. In this analysis these factors are separated using a simple model of sky radiance as the sum of a uniform background and a circumsolar component. The predictions of the model are tested against standard distributions of radiance and measured shade-ring corrections for clear skies. The model is also used to describe average distributions of radiance for cloudy skies and is in good agreement with the limited measurements available. This analysis enables measurements of solar radiation to be partitioned more exactly into direct and diffuse components and may also be applicable to the estimation of diffuse irradiance on other shaded surfaces.