Hertzsprung-Russell diagram tracks of our 30 and 60 M_⊙ model subjected to different mass-loss rates which are kept fixed during the core-He-burning RSG phase. No mass loss is applied till log(T_eff)=3.7 below which the models are subjected to a constant mass-loss rate specified in the legend. The luminosity of RSGs during core-He burning is primarily determined by the He core mass, which remains largely insensitive to the mass-loss rate.