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 \mathrm { Z } = 0.008 and \mathrm { Z } = 0.004 , corresponding to the observed metallicities of the Large and Small Magellanic Clouds , respecitively .
Third dredge-up occurs in stars of 1 M _ { \mathrm { \odot } } and above and carbon stars were found for models between 1 M _ { \mathrm { \odot } } and 3 M _ { \mathrm { \odot } } .
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 can not be produced from our detailed models unless the minimum core mass for third dredge-up is reduced by 0.06 M _ { \mathrm { \odot } } .