In this work we present a systematic investigation of the thermoelectric properties of semiconductor alloys. Electronic properties (Fermi energy, Seebeck coefficient, and electrical resistivity) are calculated in both extrinsic and intrinsic regimes using the nearly-free-electron approximation and the Fermi-Dirac statistics. The lattice thermal conductivity is computed by including anharmonic phonon interactions rigorously. The thermal conductivity contributions from donor electrons, and electron-hole pairs are also taken into account. We successfully explain the previously reported experimental measurements of the magnitude as well as temperature dependence of the electronic and thermal transport coefficients, as well as the thermoelectric figure of merit ZT for the Bi-2(Te0.85Se0.15)(3) single crystal with 0.1 wt % CuBr and 0.2 wt % SbI3 dopants. The frequency dependence of thermal conductivity is investigated in detail for a 0.2 wt % SbI3-doped sample at several temperatures. Furthermore, the effect of alloying on the thermoelectric efficiency of (Bi2Te3)(x)(Bi2Se3)((1-x)) single crystals is explored.