These quaternary chalcogenides are isostructural, crystallizing in a unique structure type comprising localized Cu clusters and Te(2)(2-) dumbbells. With less than six Cu atoms per formula unit, these materials are p-type narrow-gap semiconductors, according to the balanced formula Ba(2+)(Cu(+))6Q(2-)(Te(2)(2-))3 with Q = S, Se. Encouraged by the outstanding thermoelectric performance of Cu(2-x)Se and the low thermal conductivity of cold-pressed BaCu(5.7)Se(0.6)Te(6.4), we determined the thermoelectric properties of hot-pressed pellets of BaCu(5.9)STe(6) and BaCu(5.9)SeTe(6). Both materials exhibit a high Seebeck coefficient and a low electrical conductivity, combined with very low thermal conductivity below 1 W m(-1) K(-1). Compared to the sulfide-telluride, the selenide-telluride exhibits higher electrical and thermal conductivity and comparable Seebeck coefficient, resulting in superior figure-of-merit values zT, exceeding 0.8 at relatively low temperatures, namely, around 600 K.