We explain recent experimental findings on Tl-doped Bi2Se3 by determining the electronic and transport properties by first-principles calculations and semi-classical Boltzmann theory. Though Tl-doping introduces a momentum-dependent spin-orbit splitting, the effective mass of the carriers is essentially not modified, while the band gap is reduced. Tl is found to be exceptional in this respect as other dopants modify the dispersion, which compromises thermoelectricity. Moreover, we demonstrate that only after Tl-doping strain becomes an efficient tool for enhancing the thermoelectric performance. A high figure of merit of 0.86 is obtained for strong p-doping (7 × 10^20 cm^(−3), maximal power factor) at 500 K under 2% tensile strain.