Thermoelectric generators can convert heat directly into usable electric power but suffer from low efficiencies and high costs, which have hindered wide-scale applications. Accordingly, an important goal in the field of thermoelectricity is to develop new high performance materials that are composed of more earth abundant elements. The best systems for midtemperature power generation rely on heavily doped PbTe, but the Te in these materials is scarce in the Earth's crust. PbSe is emerging as a less expensive alternative to PbTe, although it displays inferior performance due to a considerably smaller power factor S-2 sigma, where S is the Seebeck coefficient and sigma is electrical conductivity. Here, we present a new p-type PbSe system, Pb0.98Na0.02Se-x%HgSe, which yields a very high power factor of similar to 20 mu W.cm(-1).K-2 at 963 K when x = 2, a 15% improvement over the best performing PbSe-x%MSe materials. The enhancement is attributed to a combination of high carrier mobility and the early onset of band convergence in the Hg-alloyed samples similar to 550 K), which results in a significant increase in the Seebeck coefficient. Interestingly, we find that the Hg2+ cations sit at an off-centered position within the PbSe lattice, and we dub the displaced Hg atoms "discordant". DFT calculations indicate that this feature plays a role in lowering thermal conductivity, and we believe that this insight may inspire new design criteria for engineering high performance thermoelectric materials. The high power factor combined with a decrease in thermal conductivity gives a high figure of merit ZT of 1.7 at 970 K, the highest value reported for p-type PbSe to date.