By use of a new method that allows for an analysis of stellar evolution with a minimum of model dependency, we discuss the conditions for progenitors of UV-bright asymptotic giant branch (AGB) manque stars to form in galaxies of various metallicities. UV-bright manque stars in the so-called slow blue phase have been suggested as the explanation for the observed excess of UV flux shortward of almost-equal-to 3000 angstrom in metal-rich elliptical galaxies relative to metal-poor systems. We find that in systems where the ratio of helium enrichment relative to metallicity enrichment, R = DELTAY/DELTAZ, is close to the solar value, the possible UV-bright manque stars will give rise to UV radiation which is almost independent of metallicity. Only for systems with values of R slightly bigger than the solar value will the predicted relative number of manque stars be a strongly increasing function of metallicity. For such values of R, the increasing UV radiation behaves, qualitatively, as a function of metallicity, as it is observed in the metal-rich elliptical galaxies. In particular, we comment on a series of assumed ZAHB models published recently that were identified as potential progenitors for the ''slow blue'' AGB manque stars. We find that only those of the ZAHB models that have R slightly above the solar value can have evolved into the horizontal-branch phase within the present age of the universe (with a reasonable amount of mass loss at the red giant branch), and also only these stars show the necessary functional number increase with metallicity.