The mystery of producing strong compositional diversity among suites of comagmatic igneous rocks is investigated by considering the dynamic evolution of basaltic magma in a sheet-like chamber. A central conclusion is that inward-progressing crystallization produces strong viscosity and temperature gradients that promote convection only near the leading edge of the upper thermal boundary layer. Convection is apparently confined to an essentially isoviscous, isothermal region that hugs the downward-growing roof zone. Strong changes in viscosity with crystallization divide the upper and lower thermal boundary layers into regions of decreasing viscosity and crystallinity (N) called "rigid crust" (N ≥ 0.5), "mush" (0.5 ≥ N ≥ 0.25), and "suspension" (N ≤ 0.25). The strong increase in viscosity near the mush-suspension interface acts as a capture front that overtakes and traps slowly settling crystals. Initial phenocrysts mostly escape capture, but crystals nucleated and grown in the suspension zone can escape only if the capture front slows to a critical rate attainable only in bodies thicker than about 100 m. Escaping crystals are redistributed and sorted by convection driven by the advance of the capture front itself. Crystal-laden plumes traverse the central, hot core of the body and deposit partially resorbed and sorted crystals within the lower suspension zone. Convection is never vigorous but is part of an overall intimate balance between roofward heat loss, rigid-crust growth, crystallization kinetics, and transport and sorting of sinking escaped crystals. There is a strong similarity between these processes and those producing both varves and saline pan deposits. It is clear that lavas, lava lakes, and sills are indeed examples of true magma chambers strongly exhibiting certain aspects of this over-all process. These aspects commonly also characterize the large mafic magmatic bodies. Because strong compositional changes in the residual melt occur largely outward (that is, at lower temperatures and higher crystallinities) of the capture front, which is immobile and mostly within rigid crust, the possible range in comagmatic compositions available for eruption anywhere within the active magma is very limited. This is in broad agreement with the compositional range observed in basaltic lava lakes, sills, and plutons like Skaergaard. The tuning of convection, crystallization kinetics, and phase equilibria in chambers of this type can produce a variety of textures and layering but not a diversity of compositions.