  A long standing problem with asymptotic giant branch (AGB) star models has
been their inability to produce the low-luminosity carbon stars in the Large
and Small Magellanic Clouds. Dredge-up must begin earlier and extend deeper. We
find this for the first time in our models of LMC metallicity. Such features
are not found in our models of SMC metallicity. The fully implicit and
simultaneous stellar evolution code STARS has been used to calculate the
evolution of AGB stars with metallicities of Z=0.008 and Z=0.004, corresponding
to the observed metallicities of the Large and Small Magellanic Clouds,
respecitively. Third dredge-up occurs in stars of 1Msol and above and carbon
stars were found for models between 1Msol and 3Msol. We use the detailed models
as input physics for a population synthesis code and generate carbon star
luminosity functions. We now find that we are able to reproduce the carbon star
luminosity function of the LMC without any manipulation of our models. The SMC
carbon star luminosity function still cannot be produced from our detailed
models unless the minimum core mass for third dredge-up is reduced by 0.06Msol.
