Our understanding of the evolution of Central Stars of Planetary Nebulae (CPN) has made considerable progress during the last years. This was possible since consistent computations through the asymptotic giant branch (AGB), with thermal pulses and (in some cases) mass loss taken into account, became available (Schönberner, 1979, 1983; Kovetz and Harpaz, 1981; Harpaz and Kovetz, 1981; Iben, 1982, 1984; Wood and Faulkner, 1986). It turned out that the evolution depends very sensitively on the inital conditions on the AGB. More precisely, the evolution of an AGB remnant is a function of the phase of the thermal-pulse cycle during which this remnant was created on the tip of the AGB by the planetary-nebula (PN) formation process (Iben, 1984, 1987). This was first shown by Schönberner (1979), and then fully explored by Iben (1984). In short, two major modes of PAGB evolution to the white dwarf stage are possible, according to the two main phases of a thermally pulsing AGB star: the hydrogen-burning or helium-burning mode. If, for instance, the PN formation, i.e. the removal of the stellar envelope by mass loss, happens during a luminosity peak that follows a thermal pulse of the helium-burning shell, the remnant leaves the AGB while still burning helium as the main energy supplier (Härm and Schwarzschild, 1975). On the other hand, PN formation may also occur during the quiescent hydrogen-burning phase on the AGB, and the remnant continues then to burn mainly hydrogen on its way to becoming a white dwarf.