The solid-state transformation phenomena of spinodal decomposition and nucleation and growth are presented as tools to create nanostructured thermoelectric materials with very low thermal conductivity and greatly enhanced figure of merit. The systems (PbTe)(1-x)(PbS)(x) and (Pb(0.95)Sn(0.05)Te)(1-x)(PbS)(x) are not solid solutions but phase separate into PbTe-rich and PbS-rich regions to produce coherent nanoscale heterogeneities that severely depress the lattice thermal conductivity. For x > approximately 0.03 the materials are ordered on three submicrometer length scales. Transmission electron microscopy reveals both spinodal decomposition and nucleation and growth phenomena the relative magnitude of which varies with x. We show that the (Pb(0.95)Sn(0.05)Te)(1-x)(PbS)(x) system, despite its nanostructured nature, maintains a high electron mobility (>100 cm(2)/V x s at 700 K). At x approximately 0.08 the material achieves a very low room-temperature lattice thermal conductivity of approximately 0.4 W/m x K. This value is only 28% of the PbTe lattice thermal conductivity at room temperature. The inhibition of heat flow in this system is caused by nanostructure-induced acoustic impedance mismatch between the PbTe-rich and PbS-rich regions. As a result the thermoelectric properties of (Pb(0.95)Sn(0.05)Te)(1-x)(PbS)(x) at x = 0.04, 0.08, and 0.16 were found to be superior to those of PbTe by almost a factor of 2. The relative importance of the two observed modes of nanostructuring, spinodal decomposition and nucleation and growth, in suppressing the thermal conductivity was assessed in this work, and we can conclude that the latter mode seems more effective in doing so. The promise of such a system for high efficiency is highlighted by a ZT approximately 1.50 at 642 K for x approximately 0.08.