Structural alpha-relaxation times, tau(alpha), determined by fitting Brillouin scattering spectra of supercooled liquids to stretched exponential or Cole-Davidson phenomenological relaxation functions can produce values which diverge from the results obtained by other methods as T approaches the glass transition temperature. This apparent separation of timescales has been shown to arise in CKN from the neglect of beta-relaxation. Guided by the mode coupling theory, a memory function which includes both alpha- and beta-relaxation was constructed empirically from depolarized light scattering spectra. This memory function was found to fit the data as well as the alpha-relaxation-only models, without requiring unphysically small tau(alpha) values. It is shown how the neglect of beta-relaxation generally leads to underestimation of tau(alpha), and an alternative method of incorporating beta-relaxation in cases where the empirical model is inapplicable is described. Also, the question of alpha-scale universality is briefly discussed.