The prediction of viscosity in silicate melts, over the range of conditions found in nature, remains one of the most challenging and elusive goals in Earth Sciences. We present a strategy for fitting non-Arrhenian models [e.g., Vogel-Tammann-Fulcher (VTF) or Adam-Gibbs (AG)] to viscosity data that can be employed toward a full multicomponent model for melt viscosity. Our postulate is that the high-T viscosities of silicate melts converge to a common value. The implications are twofold. First, the number of composition-dependent parameters is reduced by a third. Second, our optimization constrains the experimentally inaccessible, high-T properties of silicate melts. The high-T limits to melt viscosity are constrained by the VTF and AG models to between 10−4.3±0.74 and 10−3.2±0.66 Pa·s, respectively, and overlap in the interval 10−3.86 to 10−3.56 Pa·s.