We study the dynamics of the glass formers toluene and glycerol below the glass transition temperature T-g by means of H-2 NMR techniques. Whereas for toluene a slow beta-process is observed in dielectric spectroscopy, this process is not discernible in glycerol. We demonstrate that standard 1D and 2D NMR experiments cannot resolve the motional process because very small angular amplitudes are involved. However, applying the solid-echo technique and varying the interpulse delay, we detect changes of the spectra for toluene but not for glycerol, Performing simulations, we estimate molecular reorientation of about 6 degrees. We conclude that the beta-process in simple organic glasses originates from highly restricted molecular reorientation of essentially all molecules. No indications for "islands of mobility" are found.