Te/Sb/Ge/Ag (TAGS) materials with rather high concentrations of cation vacancies exhibit improved thermoelectric properties as compared to corresponding conventional TAGS (with constant Ag/Sb ratio of 1) due to a significant reduction of the lattice thermal conductivity. There are different vacancy ordering possibilities depending on the vacancy concentration and the history of heat treatment of the samples. In contrast to the average α-GeTe-type structure of TAGS materials with cation vacancy concentrations <∼3%, quenched compounds like Ge0.53Ag0.13Sb0.27□0.07Te1 and Ge0.61Ag0.11Sb0.22□0.06Te1 exhibit "parquet-like" multidomain nanostructures with finite intersecting vacancy layers. These are perpendicular to the pseudocubic <111> directions but not equidistantly spaced, comparable to the nanostructures of compounds (GeTe)nSb2Te3. Upon heating, the nanostructures transform into long-periodically ordered trigonal phases with parallel van der Waals gaps. These phases are slightly affected by stacking disorder but distinctly different from the α-GeTe-type structure reported for conventional TAGS materials. Deviations from this structure type are evident only from HRTEM images along certain directions or very weak intensities in diffraction patterns. At temperatures above ∼400 °C, a rock-salt-type high-temperature phase with statistically disordered cation vacancies is formed. Upon cooling, the long-periodically trigonal phases are reformed at the same temperature. Quenched nanostructured Ge0.53Ag0.13Sb0.27□0.07Te1 and Ge0.61Ag0.11Sb0.22□0.06Te1 exhibit ZT values as high as 1.3 and 0.8, respectively, at 160 °C, which is far below the phase transition temperatures. After heat treatment, i.e., without pronounced nanostructure and when only reversible phase transitions occur, the ZT values of Ge0.53Ag0.13Sb0.27□0.07Te1 and Ge0.61Ag0.11Sb0.22□0.06Te1 with extended van der Waals gaps amount to 1.6 at 360 °C and 1.4 at 410 °C, respectively, which is at the top end of the range of high-performance TAGS materials.