Upper panel: behaviour of M_cHe at the RGB tip as a function of the initial mass for the scaled-solar Z = 10^-5 chemical composition, and for both canonical (no convective core overshooting along the MS) and non-canonical (convective core overshooting along the MS) stellar models. Solid and short dashed lines correspond to the present calculations, the long dashed line to the results by Cassisi et al. (1997). Lower panel: as in the upper panel, but for the trend of the stellar surface luminosity with mass at the RGB tip.