The order of substrate interaction with a cotransport carrier is studied by numerically fitting theoretical models to empirical data for a Na+-D-glucose pathway. Our analysis is based on a least-squares minimization routine developed at CERN, and uses data derived from tracer flux of substrate under equilibrium exchange conditions. Random, Ordered mirror, and Ordered glide models are considered and the applicability of both Random and Glide systems to the experimental observations is demonstrated. A more detailed study of the Glide model provides an estimation of the relative values of the individual rate constants describing each kinetic step in the mechanism. We argue that parameterization of competing models can result in tests which will distinguish between them, even when these contain many unknowns in the proposed structure of the kinetic mechanism. The essence of this means of model discrimination is the ability to find a single set of parameter values that fits a variety of experimental observations. The ability to obtain numerical estimates of obtain numerical estimates of individual rate constants is also a useful tool in investigation of the kinetic fine structure of the carrier. For the data at hand we conclude that a complete parameterization of the Glide model cannot be attained, possibly due to a heterogeneity in the temperature at which the experiments have been performed. Three solutions to the Glide model are presented, each of which corresponds to a fit of the Glide model to a subset of the experimental data.