The Campanian Ignimbrite is a > 200 km3 trachyte–phonolite pyroclastic deposit that erupted at 39·3 ± 0·1 ka within the Campi Flegrei west of Naples, Italy. Here we test the hypothesis that Campanian Ignimbrite magma was derived by isobaric crystal fractionation of a parental basaltic trachyandesitic melt that reacted and came into local equilibrium with small amounts (5–10 wt%) of crustal rock (skarns and foid-syenites) during crystallization. Comparison of observed crystal and magma compositions with results of phase equilibria assimilation–fractionation simulations (MELTS) is generally very good. Oxygen fugacity was approximately buffered along QFM + 1 (where QFM is the quartz–fayalite–magnetite buffer) during isobaric fractionation at 0·15 GPa (&ap; 6 km depth). The parental melt, reconstructed from melt inclusion and host clinopyroxene compositions, is found to be basaltic trachyandesite liquid (51·1 wt% SiO 2 , 9·3 wt% MgO, 3 wt% H 2 O). A significant feature of phase equilibria simulations is the existence of a pseudo-invariant temperature, ∼883 °C, at which the fraction of melt remaining in the system decreases abruptly from ∼ 0·5 to < 0·1. Crystallization at the pseudo-invariant point leads to abrupt changes in the composition, properties (density, dissolved water content), and physical state (viscosity, volume fraction fluid) of melt and magma. A dramatic decrease in melt viscosity (from 1700 Pa s to ∼ 200 Pa s), coupled with a change in the volume fraction of water in magma (from ∼ 0·1 to 0·8) and a dramatic decrease in melt and magma density acted as a destabilizing eruption trigger. Thermal models suggest a timescale of ∼ 200 kyr from the beginning of fractionation until eruption, leading to an apparent rate of evolved magma generation of about 10−3 km3/year. In situ crystallization and crystal settling in density-stratified regions, as well as in convectively mixed, less evolved subjacent magma, operate rapidly enough to match this apparent volumetric rate of evolved magma production.