The stars in the Magellanic Clouds with the largest degree of obscuration are used to probe the highly uncertain physics of stars in the asymptotic giant branch (AGB) phase of evolution. Carbon stars in particular provide key information on the amount of third dredge-up and mass-loss. We use two independent stellar evolution codes to test how a different treatment of the physics affects the evolution on the AGB. The output from the two codes is used to determine the rates of dust formation in the circumstellar envelope, where the method used to determine the dust is the same for each case. The stars with the largest degree of obscuration in the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC) are identified as the progeny of objects of initial mass 2.5-3 M⊙ and ˜1.5 M⊙, respectively. This difference in mass is motivated by the difference in the star formation histories of the two galaxies, and offers a simple explanation of the redder infrared colours of C-stars in the LMC compared to their counterparts in the SMC. The comparison with the Spitzer colours of C-rich AGB stars in the SMC shows that a minimum surface carbon mass fraction X(C) ˜ 5 × 10-3 must have been reached by stars of initial mass around 1.5 M⊙. Our results confirm the necessity of adopting low-temperature opacities in stellar evolutionary models of AGB stars. These opacities allow the stars to obtain mass-loss rates high enough (≳10-4 M⊙ yr-1) to produce the amount of dust needed to reproduce the Spitzer colours.