Thermoelectric generators, which directly convert heat into electricity, have long been relegated to use in space-based or other niche applications, but are now being actively considered for a variety of practical waste heat recovery systems-such as the conversion of car exhaust heat into electricity. Although these devices can be very reliable and compact, the thermoelectric materials themselves are relatively inefficient: to facilitate widespread application, it will be desirable to identify or develop materials that have an intensive thermoelectric materials figure of merit, zT, above 1.5 (ref. 1). Many different concepts have been used in the search for new materials with high thermoelectric efficiency, such as the use of nanostructuring to reduce phonon thermal conductivity(2-4), which has led to the investigation of a variety of complex material systems(5). In this vein, it is well known(6,7) that a high valley degeneracy (typically <= 6 for known thermoelectrics) in the electronic bands is conducive to high zT, and this in turn has stimulated attempts to engineer such degeneracy by adopting low-dimensional nanostructures(8-10). Here we demonstrate that it is possible to direct the convergence of many valleys in a bulk material by tuning the doping and composition. By this route, we achieve a convergence of at least 12 valleys in doped PbTe(1-x)Se(x) alloys, leading to an extraordinary zT value of 1.8 at about 850 kelvin. Band engineering to converge the valence (or conduction) bands to achieve high valley degeneracy should be a general strategy in the search for and improvement of bulk thermoelectric materials, because it simultaneously leads to a high Seebeck coefficient and high electrical conductivity.