In order to retrieve reliable estimates of the fractional cloud cover for two-layered cloud systems, the spatial coherence method generally requires imagery data containing observations of thermal emission at widely separated wavelengths. As the observations of thermal emission in the currently available imagery data are at 3.7 and 11 μm and as solar reflection contaminates the observations at 3.7 μm during the day, spatial coherence retrievels for two-layered systems are in general limited to data taken at night. Here we develop a retrieval scheme that uses only 11-μm radiances to obtain the cloud cover for single- and two-layered systems and therefore provides similar results for daytime and nighttime observations. To develop this retrievel method, we collect observations for an ensemble of single- and two-layered cloud systems for which the spatial coherence method provides reliable retrievals of the cloud cover. We use this ensemble to study the relationship between the number of cloud-free pixels, the number of completely cloud-covered pixels, and the fractional cloud cover for (250 km)2 regions. We discover that when the cloud cover is extensive within (250 km)2 regions, pixels which are partially cloud covered are generally heavily covered. Likewise, when (250 km)2 regions are largely cloud-free, pixels which are partially covered generally have little cover. Evidently, for the ensemble of cloud systems studied here the factors governing the large-scale cloud cover also govern the cloud cover on scales approaching the resolution of the observations (8 km)2. We use this observation to construct a retrievel method which, though it may fail to provide reliable retrievals in individual cases, will provide reliable statistics of the cloud cover for ensembles of cases. Although this statistical retrieval is applied to single- and two-layered systems here, the principles on which it is based seem to warrant more general usage.