A global data set of cloud occurrence probability derived from Moderate Resolution Imaging Spectroradiometer (MODIS) Terra and Aqua gridded daily data is analyzed to investigate the probability of obtaining at least a minimum number of cloud-free observations within various compositing periods. The probabilities derived from Terra and Aqua, with morning and afternoon overpass times, respectively, are similar and increase with compositing period. Compositing both Terra and Aqua observations results in considerably higher probabilities of obtaining a sufficient number of observations for bidirectional reflectance model-based compositing. Given that the only alternative to obtaining sufficient samples is to extend the observation period, which can cause significant problems when the surface state changes, it is concluded that using data from the two MODIS sensors provides the most effective way of generating composited products. Findings with respect to the availability of cloud-free composites when n-day composites are generated on a temporally overlapping daily rolling basis, i.e., every day, rather than every n-days, are also discussed for regional and global applications