We have used neutron activation and electron-probe fused-bead techniques to analyze the bulk major and trace-element compositions of 104 named HED meteorites (about 100–102 distinct meteorites, depending upon pairings), including 32 polymict eucrites, 30 howardites and six diogenites. Most were not previously analyzed for siderophile trace elements; many not even for major elements. Our typical sample was ∼350 mg, and in some cases two separate chips were analyzed as a test of meteorite heterogeneity. Meteorites with extraordinary compositions include Bluewing 001, an unequilibrated eucrite that is rich in Ti, Sm and other incompatible elements; Y-791192, a cumulate-dominated polymict eucrite; and LEW 87002, an oddly Sm-rich howardite dominated by a ferroan variety of diogenite. The eucrite:diogenite mixing ratio is the single most important factor determining the compositions of polymict HEDs, but wide ranges in eucrite incompatible element contents, in diogenite Cr and V contents, and in Sc contents of both eucrites and diogenites, make for diversity among the polymict HEDs. As our new siderophile data help to show, the common practice of describing the entire class of howardites as regolith breccias is erroneous. Most howardites are fragmental breccias showing no sign of origin from true (in the lunar sense, i.e., soil-like) near-surface regolith. Howardites are highly diverse in Ni content, often remarkably Ni-poor, compared to lunar regolith breccias. However, the few (8) howardites with between 300 and 1200 μg/g Ni consistently show some combination of other traits suggestive of regolith origin. Most importantly, all four cases (or five if we include Malvern, which appears to have been altered by annealing) of howardites known to have enrichments in solar-wind noble gases belong to the >300 μg/g Ni group. In many cases, an abundance of glasses, particularly in spheroidal or turbid-brown form, provides additional evidence for regolith origin. We propose that the important subset of howardites that are regolith breccias be formally distinguished by the designation regolithic howardite. Apart from high siderophile levels, the regolithic howardites are compositionally distinctive in having Al 2O 3 consistently near 8–9 wt%; corresponding to a eucrite:diogenite mixing ratio of precisely 2:1. Assuming the HEDs are reasonably representative of the ancient (i.e., pre-vestoid-launch) surface of Vesta, this clustering of regolith composition is difficult to explain unless most of the ancient diogenite component was brought to the surface in a single early episode (i.e., probably a single great impact), after which smaller-scale cratering (with no further major excavations of diogenite until the vestoid-forming event), efficiently homogenized the surface. Such a single-excavation model may also help to explain why diogenites, in marked contrast with eucrites, are seldom polymict; and why Al 2O 3-poor (diogenite-dominated) howardites consistently lack major siderophile enrichments. The low siderophile contents of polymict eucrites are most enigmatic. Possibly in the HED-asteroidal context (low collision velocities, etc.), only materials blended by multiple impacts consistently acquire major enrichments in siderophile elements.