  This study calls attention to the importance of properly coupling the
molecular opacities to the actual surface abundances of TP-AGB stars that
experience the third dredge-up and/or hot-bottom burning, i.e. with surface
abundances of carbon and oxygen varying with time. New TP-AGB calculations with
variable opacities -- replacing the usually adopted solar-scaled opacity tables
-- have proven to reproduce, for the first time, basic observables of carbon
stars, like their effective temperatures, C/O ratios, and near-infrared
colours. Moreover, it turns out that the effect of envelope cooling -- due to
the increase in molecular opacities -- may cause other important effects,
namely: i) shortening of the C-star phase; ii) possible reduction or shut-down
of the third dredge-up in low-mass carbon stars; and iii) weakening or even
extinction of hot-bottom burning in intermediate-mass stars.
