The spin-lattice relaxation time T-1 of simple organic glass formers is analyzed by introducing a spectral density obtained from broadband dielectric susceptibility data chi "(omega). For this purpose chi "(omega) was measured for several glass formers, that do not exhibit a Johari-type secondary relaxation process, covering a frequency range between 10(-2) Hz and 10(9) Hz at temperatures above and below the glass transition temperature T-g. We introduce an analytical function to fit the shape of the main relaxation (alpha-process) above T-g, in particular taking into account high-frequency contributions in chi "(omega) commonly known as high-frequency wing. Below T-g the latter feature appears as a power law susceptibility chi "(omega)proportional to omega(-gamma), with gamma < 0.1 and a characteristic temperature dependence chi "(T)proportional to exp(T/const.), yielding almost 1/omega behavior in the spectral density. On the base of this complete description of chi "(omega), a quantitative comparison of dielectric and NMR spectroscopy is possible, which is carried out in full detail for glycerol-d(3) (H-2-NMR), yielding almost identical spectral densities at the Larmor frequency in both cases. In particular the temperature dependence of the high-frequency wing reappears in that of the spin lattice relaxation rate. In addition a semiquantitative analysis is given for trinaphthyl benzene (H-1-NMR) and tricresyl phosphate (P-31-NMR).