Reparametrization of the measurement model can be very useful in finding the best fit to impedance spectroscopy data of electrochemical systems. When the recently proposed generalized mathematical model approach is used instead of the commonly used equivalent circuit approach, the sensitivity of fitting computations on initial estimates of model parameters is strikingly small. A reduction in sensitivity of several orders of magnitude has been noticed. In both approaches the model is in principle the same. It differs only in the type of parameters. Also, the fitting of any model to impedance spectroscopy data, at least in the case when they contain errors, leads to different global minimum fits, depending on the fitting system used : Y or Z. Both effects are interpreted in terms of the recently discussed non-linearity of models of electrochemical systems. Parameter and intrinsic non-linearity have been distinguished. The effect of model reparametrization on computational sensitivity to the initial parameter estimates is ascribed to differences in parameter non-linearity of the model for various possible types of parameters. The effect of the choice of fitting procedure (Z or Y system) on the fit minimum is ascribed to a difference in the intrinsic non-linearity of the model, namely when this is used in its Z or Y form.