Dielectric loss spectra of glass forming liquids are analyzed, with emphasis on systems for which a peak due to a secondary relaxation is not immediately obvious. Thus, glass formers are considered for which the high-frequency flank of the alpha-relaxation peak appears to be dominated by a so-called wing contribution. It is shown that even for such supercooled liquids the shape of the alpha-peak has to be characterized by two parameters. By performing a series of aging experiments it is demonstrated that the high-frequency flank of the alpha-relaxation, assumed to follow a power-law behavior, is superimposed by contributions from an excess wing and from a beta-relaxation peak. In particular, the excess wing, previously associated with either the alpha- or the beta-relaxation, is identified as a feature that evolves in its own right. It is argued that excess wing and beta-relaxation are always present albeit with relative strengths that may vastly differ from glass former to glass former.