Black paints are commonly used to provide broadband light absorbers in high-precision optics. We show how multidielectric coatings improve the performances of these absorbers. The coated rough paints still exhibit a quasi-lambertian diffuse reflection, but this scattering pattern can be reduced by several orders of magnitude, which strongly enhances absorption. Predictions are based on an exact electromagnetic theory of light scattering from arbitrary rough multilayers. Results are also compared to useful approximate theories.