The upper bound for the production of uniform amorphous ribbons during free-jet melt spinning is predicted by coupling a mass balance condition for the melt-pool with a simple boundary layer model for momentum transfer. The relationships between melt-pool length, ribbon thickness and wheel speed are investigated, and a criterion is developed for the onset of unsteady melt-pool behavior, which has previously been associated with increased surface roughness, porosity, and the formation of crystalline phases at high wheel speeds.