Theoretical calculations of intensity of scattered light and observations of absolute phase functions of brightness in the clear-sky atmosphere are used as a basis to propose methods for selecting data of monitoring measurements of sky brightness, presented at AERONET sites, aimed at eliminating cloudy situations. The methods are based on the following condition. Scattering of solar light in the clear-sky atmosphere occurs on the system of particles of a wide size spectrum what excludes the manifestations of lobe structure of the scattering phase function. A number of CIMEL photometer sites of brightness observations, located in deserts, woodlands, oceanic islands, and Russian cities, use the selection of observation data to eliminate cloudy situations. Small percentage of clear-sky days has been recorded in the oceans.