The optical spectra of a number of organic compounds have been examined in low-temperature, glassy solutions. According to the experimental conditions of excitation, a given sample can yield either the usual broad bands complete with Stokes shift or a set of very narrow fluorescence lines (~1 cm-1). Our comparisons of these two distinct types of spectra from the same sample make it possible to explain such features of the conventional spectra as their broad bandwidths, peak positions, and Stokes shifts.