Lead chalcogenide thermoelectric systems have been shown to reach record high figure of merit values via modification of the band structure to increase the power factor or via nanostructuring to reduce the thermal conductivity. Recently, (PbTe)(1-x)(PbSe)(x) was reported to reach high power factors via a delayed onset of interband crossing. Conversely, the (PbTe)(1-x)(PbS)(x) was reported to achieve low thermal conductivities arising from extensive nanostructuring. Here we report the thermoelectric properties of the pseudoternary 2% Na-doped (PbTe)(1-2x)(PbSe)(x)(PbS)(x) system. The (PbTe)(1-2x)(PbSe)(x)(PbS)(x) system is an excellent platform to study phase competition between entropically driven atomic mixing (solid solution behavior) and enthalpy-driven phase separation. We observe that the thermoelectric properties of the PbTe-PbSe-PbS 2% Na doped are superior to those of 2% Na-doped PbTe-PbSe and PbTe-PbS, respectively, achieving a ZT approximate to 2.0 at 800 K. The material exhibits an increased the power factor by virtue of valence band modification combined with a very reduced lattice thermal conductivity deriving from alloy scattering and point defects. The presence of sulfide ions in the rock-salt structure alters the band structure and creates a plateau in the electrical conductivity and thermopower from 600 to 800 K giving a power factor of 27 mu H/cmK(2). The very low total thermal conductivity values of 1.1 W/m.K of the x = 0.07 composition is accounted for essentially by phonon scattering from solid solution defects rather than the assistance of endotaxial nanostructures.