The alloys (GeTe)(x)(AgSbTe2)(100-x), commonly known as TAGS-x, are among the best performing p-type thermoelectric materials for the composition range 80 <= x <= 90 and in the temperature range 200-500 degrees C. They adopt a rhombohedrally distorted rocksalt structure at room temperature and are reported to undergo a reversible phase transition to a cubic structure at similar to 250 degrees C. However, we show that; for the optimal x = 85 composition (TAGS-85), both the structural and thermoelectric properties are highly sensitive to the initial synthesis method employed. Single-phase rhombohedral samples exhibit the best thermoelectric properties but can only be obtained after an annealing step at 600 degrees C during initial Cooling from the melt. Under faster cooling conditions, the samples obtained are inhomogeneous, containing multiple rhombohedral phases with a range of lattice parameters and exhibiting inferior thermoelectric properties. We also find that when the room-temperature rhombohedral phase is heated, an intermediate trigonal structure containing ordered cation vacancy layers is formed at similar to 200 degrees C, driven by the spontaneous precipitation of argyrodite-type Ag8GeTe6 which alters the stoichiometry of the TAGS-85 matrix. The rhombohedral and trigonal phases of TAGS-85 coexist up to 380 degrees C, above which a single cubic phase is obtained and the Ag8GeTe6 precipitates redissolve into the matrix. On subsequent cooling a mixture of rhombohedral, trigonal, and Ag8GeTe6 phases is again obtained. Initially single-phase samples exhibit thermoelectric power factors of up to 0.0035 W m(-1) K-2 at 500 degrees C, a value that is maintained on subsequent thermal cycling and which represents the highest power factor yet reported for undoped TAGS-85. Therefore, control over the structural homogeneity of TAGS-85 as demonstrated here is essential in order to optimize the thermoelectric performance.