Thermoelectric materials can provide sources of clean energy and increase the efficiency of existing processes. Solar energy, waste heat recovery, and climate control are examples of applications that could benefit from the direct conversion between thermal and electrical energy provided by a thermoelectric device. The widespread use of thermoelectric devices has been prevented by their lack of efficiency, and thus the search for high-efficiency thermoelectric materials is ongoing. Here we describe our initial efforts studying copper-containing ternary compounds for use as high-efficiency thermoelectric materials that could provide low-cost alternatives to their silver-containing counterparts. The compounds of interest are semiconductors that crystallize in structures that are variants of binary zincblende structure compounds. Two examples are the compounds Cu2SnSe3 and Cu3SbSe4, for which we present here preliminary thermoelectric characterization data.