Logarithm of the total mass of H (in solar units) at the point of maximum effective temperature of the cooling sequence versus the white dwarf mass. The dotted (solid) line shows the predictions from our Z = 0.0001 progenitors when overshooting during the TP-AGB is considered (neglected). In addition, we show the results for the case of an enhanced mass loss rate during the TP-AGB and the following early post-AGB phases (dashed line).