ABSTRACT The Thermally Pulsing- (Super) Asymptotic Giant Branch is a late stage in the evolution of low- and intermediate-mass stars. These stars undergo strong wind mass-loss and diverse nucleosynthesis. Third dredge-up events, that occur following thermal pulses, are responsible for enriching the surfaces of Asymptotic Giant Branch stars, hence an understanding of this process is crucial for constraining galactic chemical evolution. Using a custom numerical scheme, we investigate the temporal and spatial resolution required to resolve the third dredge-up in the 1D stellar evolution code mesa. With mesa’s default controls, the third dredge-up efficiency is underestimated by as much as $\approx 76~{{\ \rm per\ cent}}$. In stars that undergo hot third dredge-up (M ≳ 6 M⊙), the third dredge-up efficiency is overestimated by $\approx 55~{{\ \rm per\ cent}}$. The Thermally Pulsing- (Super) Asymptotic Giant Branch (TP-(S)AGB) evolution is computed for models with initial masses 1 ≤ Mi/M⊙ ≤ 8 at Solar metallicity (Z = 0.014). The minimum initial mass for carbon stars falls in the range 1.5–1.75 M⊙, compatible with observations. The use of mesa for TP-(S)AGB evolution is validated by comparison to the widely used monash models which show good agreement in the maximum third dredge-up efficiency at initial masses Mi > 2 M⊙. We also compare the third dredge-up efficiency in models produced using two independent stellar evolution codes, fruity and aton, which were computed with various differences in input physics including mass-loss, and which exhibit weaker third dredge-up episodes.