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 °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 ∼250 °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 °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 ∼200 °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 °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 °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.