If a basaltic magma is separated from its mantle source region only after a large amount of fusion, as indicated for mid-ocean ridge tholeiites by large ion lithophile (LIL) element studies, volatile-free phase relationships may be used to model closely the fusion process at the site of origin. Volatile-free solidus curves in pressure-temperature space display low-temperature cusps where subsolidus phase transitions intersect the solidus, and these cusps are believed to be important in controlling the depth of magma generation and the compositions of primary magmas. In the system CaO-MgO-Al2O3-SiO2, the solidus curve for simplified plagioclase and spinel lherzolite has been determined up to 20 kb, and a cusp has been found at 9 kb, 1300 °C, where the transition from simplified plagioclase to spinel lherzolite intersects the solidus and forms an invariant point. Simplified basaltic melts formed along the solidus curve change from quartz-normative compositions at low pressures to olivine-normative compositions at high pressures, and the composition of the first liquid produced at the 9 kb cusp resembles closely the composition of the least-fractionated mid-ocean ridge tholeiites. It is proposed that these least-fractionated basalts have been modified very little by fractional crystallization as they passed upward to the surface and are close to the composition of primary basalt generated at the mantle equivalent of the 9 kb cusp (30 km depth). Assuming a lherzolitic mantle source, the composition of this primary magma would be expected to remain fairly constant despite varying amounts of fusion as long as these amounts are between about 2 and 35 per cent, and despite variations in the proportions of minerals in the source region. For complex natural compositions in the mantle, the cusp would not be a point but would be expected to appear as a low temperature region on the solidus extending over a small pressure range at about 9 kb and 1200–1250 °C. It is suggested that magma generation at the cusp causes a sharp change in the slope of the geotherm beneath active ridges from approximately adiabatic at depths geater than about 30 km to strongly superadiabatic at depths less than 30 km. LIL element concentrations indicate that a close approach to fractional fusion is not applicable to the generation of primary magmas at spreading centers. Instead, a model involving varying amounts of equilibrium fusion is preferred, with fresh mantle being continually supplied at the 9 kb cusp as mantle material convects upward along the rising limb of a mantle convection cell. Primary magmas would thus be produced with fairly uniform major element compositions but widely different LIL element concentrations. Subsequent fractional crystallization of the primary magmas would produce most of the observed major element variations in the erupted basalts but would have only a second-order effect on the LIL element concentrations.