Dalton and Presnall (1998) and Gudfinnsson and Presnall (2003) determined the melting relations of model garnet lherzolite in the system CaO-MgO-Al₂O₃-SiO₂-CO₂ (CMAS-CO₂) at 3-8 GPa, 1245-1800°C. These phase relations comprise a divariant surface in P-T space. The high-temperature side of the surface is bounded by the solidus curve for garnet lherzolite in the CO₂-free system. At several hundred degrees lower temperature, the surface is bounded by the solidus curve for CO₂-bearing compositions as a carbonate phase joins the phase assemblage. The garnet lherzolite phase assemblage coexists with CO₂-bearing melts along the divariant surface, and continuous gradations occur between carbonatitic, kimberlitic, and melilititic melts. The carbonatite melts are generated at the lowest temperatures, while kimberlites are generated at higher temperatures as the CO₂ content of the melts decreases and the SiO₂ content increases. At a pressure below 4 GPa, the kimberlites grade into melilitites, which contain less MgO and more Al₂O₃ than the kimberlites. Parameterization of the compositions of all the phases as a function of pressure and temperature and the use of published algebraic methods allows modeling of the melting of any selected CO₂-bearing garnet lherzolite composition within the CMAS-CO₂ system, including incipient melting near the carbonate-bearing solidus. We have modeled the melting of a relatively CO₂-rich garnet lherzolite composition containing 0.15 wt % CO₂. Because of the low melting degrees involved, the melting paths closely approach solid adiabats. A relatively cool adiabat with a potential temperature (Tp) of 1310°C and a slope of 15°C/GPa intersects the carbonate-bearing solidus at a pressure of about 7 GPa, and the melting path follows the solidus for a narrow pressure range until all the carbonate is exhausted after about 0.3-0.4% melting. Melting continues in the divariant field, and at a pressure of 3 GPa only about 0.5% melting has occurred, generating carbonatitic melts only. An adiabat with a Tp of 1510°C intersects the carbonate-bearing solidus at a pressure considerably higher than the range of our data, but at 7 GPa the melt composition is about to change from carbonatitic to kimberlitic as the extent of melting has reached about 0.6-0.7%. At lower pressures, the melt changes from kimberlite to melilitite composition. Thus, elevated geotherms are needed to generate kimberlite and melilitite magmas. This requirement is lessened, however, if considerable amounts of water are present. For example, Price et al. (2000) came to the conclusion that the Jericho Pipe kimberlite magmas contained about 6% H₂O, which will lower the equilibrium temperature 200-300°C. The other most important mantle component not present in the CMAS-CO₂ system, FeO, is likely to have only small effect on kimberlite generation, but its effect on the stability of carbonates, and hence the generation of carbonatites, could be important. As carbonatite melts could become interconnected at less than 0.1 % melting (Minarik and Watson, 1995), they may be highly mobile in the upper mantle, and as they commonly carry large amounts of incompatible elements, they could have an important effect on the trace element signatures of basalt lavas (Presnall et al., 2002).