Using quasielastic neutron scattering, we compare dynamics in single-element liquids, glass-forming selenium and non glass-forming gallium. There is a single jump-diffusion process in gallium, whereas in selenium there is also a faster, spatially localized process. The fast and slow processes describe beta- and alpha-relaxation, respectively. We then analyze an archetypical glass-former, glycerol, to show that the two-component fit, with beta- and alpha-relaxations explicitly separated, yields the correct value for the translational diffusion coefficient and provides information on the spatial localization of the beta-relaxation that is not experimentally accessible otherwise. (C) 2012 Elsevier B. V. All rights reserved.