The results of multi-anvil melting experiments are reported for a range of compositions in the system CaO-MgO-Al 2 O 3 -SiO 2 . The liquidus crystallization fields for forsterite, orthopyroxene, clinopyroxene, and garnet have been mapped out at 10 GPa, as have their intersections at various cotectics. The composition of the liquid that is multiply saturated in forsterite, orthopyroxene, clinopyroxene, and garnet has been also determined to within + or -0.5-1.0 wt% (2sigma ), and the result is in excellent agreement with a previous estimate (Herzberg 1992). These experiments confirm that the effect of pressure is to reduce Al 2 O 3 and increase MgO and SiO 2 in magmas formed by the melting of garnet lherzolite with increasing pressure (Herzberg 1992). Melting experiments in the system MgO-SiO 2 also have been performed to constrain how pressure affects the compositions of liquids that are saturated in harzburgite [L+Ol+Opx]. Experiments in both CaO-MgO-Al 2 O 3 -SiO 2 and MgO-SiO 2 demonstrate that there is a maximum normative olivine content to liquids formed by initial or advanced melting of peridotite in the upper mantle, and this occurs at 7 to 8 GPa. For most peridotite that undergo decompression melting in a plume, clinopyroxene and garnet are the first crystalline phases to melt out and, with a few important but rare exceptions, the experimentally constrained liquids are unlike most volcanic rocks. Advanced anhydrous melting will yield liquids with a residual harzburgite mineralogy [L+Ol+Opx], and these liquids are similar in composition to most komatiites with Cretaceous and 2700 Myr Archaean ages.