We show an example of hierarchically designing electronic bands of PbSe toward excellent thermoelectric performance. We find that alloying 15 mol % PbTe into PbSe causes a negligible change in the light and heavy valence band energy offsets (Delta E-V) of PbSe around room temperature; however, with rising temperature it makes Delta E-V decrease at a significantly higher rate than in PbSe. In other words, the temperature-induced valence band convergence of PbSe is accelerated by alloying with PbTe. On this basis, applying 3 mol % Cd substitution on the Pb sites of PbSe0.85Te0.15 decreases Delta E-V and enhances the Seebeck coefficient at all temperatures. Excess Cd precipitates out as CdSe1-yTey, whose valence band aligns with that of the p-type Na-doped PbSe0.85Te0.15 matrix. This enables facile charge transport across the matrix/precipitate interfaces and retains the high carrier mobilities. Meanwhile, compared to PbSe the lattice thermal conductivity of PbSe0.85Te0.15 is significantly decreased to its amorphous limit of 0.5 W m(-1) K-1. Consequently, a highest peak ZT of 1.7 at 900 K and a record high average ZT of similar to 1 (400-900 K) for a PbSe-based system are achieved in the composition Pb0.95Na0.02Cd0.03Se0.85Te0.15, which are similar to 70% and similar to 50% higher than those of Pb0.98Na0.02Se control sample, respectively.