Future models for predicting the viscosity of geologically relevant silicate melts must find a means of partitioning the effects of composition across a system that shows varying degrees of non-Arrhenian temperature dependence. In the short term, the decisions governing how to expand the non-Arrhenian parameters in terms of composition will probably derive from empirical study. The non-linear character of the non-Arrhenian models ensures strong numerical correlations between model parameters which may mask the effects of composition. We present a numerical analysis of the nature and magnitudes of correlations inherent in fitting a non-Arrhenian model (e.g., Tamman-Vogel-Fulcher function) to published measurements of melt viscosity. Furthermore, we demonstrate the extent to which the quality and distribution of experimental data can affect covariances between model parameters. The extent of non-Arrhenian behaviour of the melt also affects parameter estimation. We explore this effect using albite and diopside melts as representative of strong, nearly Arrhenian melts and fragile, non-Arrhenian melts, respectively. The magnitudes and nature of these numerical correlations tend to obscure the effects of composition and, therefore, are essential to understand prior to assigning compositional dependencies to fit parameters in non-Arrhenian models.