High-efficiency thermoelectric materials require a high conductivity. It is known that a large number of degenerate band valleys offers many conducting channels for improving the conductivity without detrimental effects on the other properties explicitly, and therefore, increases thermoelectric performance. In addition to the strategy of converging different bands, many semiconductors provide an inherent band nestification, equally enabling a large number of effective band valley degeneracy. Here we show as an example that a simple elemental semiconductor, tellurium, exhibits a high thermoelectric figure of merit of unity, not only demonstrating the concept but also filling up the high performance gap from 300 to 700 K for elemental thermoelectrics. The concept used here should be applicable in general for thermoelectrics with similar band features.