Metal-rich, mixed copper-rhodium sulfide Cu3-δRh34S30 that represents a new Cu-filled variant of the Rh17S15 structure has been synthesized and structurally characterized. Copper content in the [CuRh8] cubic cluster was found to vary notably dependent on the chosen synthetic route. Full site occupancy was achieved only in nanoscaled Cu3Rh34S30 obtained by a rapid, microwave-assisted reaction of CuCl, Rh2(CH3CO2)4 and thiosemicarbazide at 300 °C in just 30 min; whereas merely Cu-deficient Cu3-δRh34S30 (2.0 ≥ δ ≥ 0.9) compositions were realized via conventional high-temperature ceramic synthesis from the elements at 950 °C. Although Cu3-δRh34S30 is metallic just like Rh17S15, the slightly enhanced metal content has a dramatic effect on the electronic properties. Whereas the Rh17S15 host undergoes a superconducting transition at 5.4 K, no signs of the latter were found for the Cu-derivatives at least down to 1.8 K. This finding is corroborated by the strongly reduced density of states at the Fermi level of the ternary sulfide and the disruption of long-range Rh-Rh interactions in favor of Cu-Rh interactions as revealed by quantum-chemical calculations.