The contribution of inelastic molecular scattering (Rayleigh-Brillouin and rotational Raman scattering) to the filling-in of Fraunhofer lines in the light of the blue sky is studied. Aerosol fluorescence is shown to be negligible, and aerosol scattering is ignored. The angular and polarization dependences of the filling-in detail for single scattering are discussed. An approximate treatment of multiple scattering, using a backward Monte Carlo technique, makes it possible to investigate the effects of the ground albedo. As the molecular scatterings alone produce more line-filling than is observed, it seems likely that aerosols dilute the effect by contributing unaltered sunlight to the observed spectra.