Ternary diamond-like semiconductors can be built-up from simple group IV, group III-V, and group II-VI diamond and zincblende structure elements and compounds by replacing single cation elements with two elements of total electron valence equal to that of the replaced atom. This process leads to the formation of new classes of semiconductors including I-III-VI2 compounds, I2-IV-VI3 compounds, and I3-V-VI4 compounds. Examples include CuGaSe2, Cu2SnSe3, and Cu3SbSe4, respectively. With increasing complexity of the unit cell the electronic band gap narrows and the lattice thermal conductivity decreases, two effects favorable for thermoelectricity. Several compounds in these families possess thermoelectric figure of merit in excess of unity. By altering the composition of these diamond-like structures, more new compounds with different bonding types and crystal structures can be formed. These “diamond-unlike” compounds possess unique features that are scientifically interesting and that provide for potential new pathways to higher figure of merit.