  The core mass-luminosity (Mc-L) relation of TP-AGB stars is a key ingredient
in synthetic calculations of their evolution. Recently, Herwig et al. (1998)
have presented full calculations of TP-AGB models with strong dredge-up
occurring already during early thermal pulses. The resulting luminosity
evolution differs appreciably from the simple linear Mc-L relation. In this
paper, we show that at least part of the luminosity evolution can be understood
as being the result of two well-known effects: the gradual approach to the
asymptotic behaviour that characterises the first thermal pulses, and the
chemical composition changes of the envelope. Both effects are already
implemented in the Mc-L relations used in synthetic models. Consequently, these
models are able to reproduce the behaviour of full calculations. Whether
additional effects, not yet taken into account, are present, can be decided
only through additional calculations and data. We also comment on the validity
of a linear Mc-L relation and its possible violation, as mentioned by Herwig et
al.
