A method for making high optical quality multicomponent chalcogenide glasses without refractive index perturbations due to striae, phase separation or crystal formation using a sealed ampoule with chemical components enclosed inside, a two-zone furnace, a convection heating/mixing step, and multiple fining steps. Initially, the sealed ampoule is oriented vertically within the two-zone furnace and heated to melt the chemical components contained within, and a temperature gradient is created between the top zone and the bottom zone such that the bottom zone has a higher temperature. This temperature gradient causes convection currents within the viscous liquid until it is sufficiently mixed due to the convective flow. Then the temperature gradient is reversed such that the top zone now has a higher temperature and the convective flow ceases. The furnace temperatures are then reduced over a period of time, with holds at multiple temperatures for fining and cooling to form a solid glass.