Relative enrichment of the surface abundance of ⁴He with respect to its initial value (in mass fraction) for Paper I models at the end of the first and second dredge-up (solid and dashed black lines, respectively) as a function of the initial stellar mass and for two metallicities (Z_⊙ and Z = 0.0001; left and right panels, respectively). Top panels: our standard predictions are compared with those of BS99 (blue circles; open and full at the end of the first and second dredge-up, respectively). Bottom panels: our models including both rotation-induced mixing and thermohaline instability are compared with the “cool-bottom processing” predictions by BS99 at the RGB tip (blue squares).