Tonalite–trondhjemite–granodiorite (TTG) magmatism provides a window into the composition of the Earth's earliest crust, and on rates of heat transfer during the Archaean. However, the tectonic setting in which these magmas form, and the physical mechanisms by which TTG melt segregates from its partially molten source rock, are poorly understood. Here we present some simple models aimed at predicting the compositions of partial melts which segregate from thickened mafic (amphibolitic or eclogitic) lower crust. Our results suggest that buoyancy-driven compaction with melt flow along grain edges can yield large volumes of segregated TTG melt over geologically realistic timescales (4000 years–10 My). Petrologic diversity is predicted even from a homogenous protolith: the chemical composition of the segregated melt varies both spatially and temporally, and is governed not only by the composition and mineralogy of the source rock, the depth of melting, and the melting reactions, but also by the physical processes through which the melt migrates and segregates from its partially molten host. This simple model represents the first step towards a properly coupled physical and chemical model of TTG formation, which is closely constrained by geochemical, field and laboratory data. Such models will compliment the existing geochemical work and help resolve some of the outstanding issues concerning TTG petrogenesis.