Plastic foils containing nonabsorbing pigments can display a high reflectance of solar radiation combined with a high transmittance in the atmospheric window region in the thermal infrared. Such foils can be applied as selective covers enabling radiative cooling of an underlying material even in direct sunlight. Extensive calculations were performed of the optical properties of nonabsorbing foils pigmented with various oxides and sulphides. The calculations were carried out by the four flux theory using input calculations for single spheres by the Lorenz-Mie theory. The optical properties of the foils were optimized for radiative cooling applications with respect to particle radius, pigment volume fraction, thickness of the foil, and refractive index of the particles. In particular, ZnS is a suitable pigment material because of its high refractive index and low infrared absorption. It should be feasible to achieve a solar reflectance of 0.9 in combination with an infrared transmittance of 0.8 to 0.85 in the atmospheric window region by foils made of a transparent matrix material pigmented with ZnS. Initial experimental studies have been performed on pigmented polyethylene foils.