Polycrystalline samples of the tetrahedrite phase Cu₁₂Sb_4-xTe_xS₁₃ with nominal compositions 0.5 <= x <= 2.0 were synthesized by two different synthesis routes: from precursors and from direct melting of elements. The crystal structure was verified by single-crystal and powder X-ray diffraction (PXRD), both confirming the successful substitution of Te for Sb in both series. Our chemical analyses evidenced differences between the chemical compositions of the two series of samples likely tied to the synthesis method employed and suggesting off-stoichiometry on the Sb site. High-temperature PXRD and differential scanning calorimetry measurements indicate that these materials are stable up to 623 K. Above this temperature, the decomposition process starts and ends up near 748 K where a Cu_2-yS-type phase is solely observed. In agreement with the simple electron counting rule and electronic band structure calculations, the electrical resistivity and thermopower increase with increasing x reflecting the gradual shift from a p-type metallic state (x = 0.0) to a p-type semiconducting behavior (x = 2.0). Combined with extremely low lattice thermal conductivity values (kappa of 0.5 W m^-1 K^-1 at 623 K), this substitution enables us to optimize the power factor leading to a maximum thermoelectric figure of merit ZT of about 0.8 at 623 K. These results parallel those obtained in prior studies dealing with partial substitutions on the Cu site and enlarge the possibilities to tune the electrical properties of tetrahedrites by extrinsic dopants.