Abstract The generality, scope, and limitations of Impedance Spectroscopy (IS) are discussed, with emphasis on unsupported conditions in ionic systems. For such conditions, the maximum reaction rate which can be determined from IS data is limited. The finite-length-Warburg diffusion frequency responses of unsupported and supported situations are simplified and compared, and similarities and differences emphasized. Two types of ambiguity possibly present in fitting IS data to equivalent circuits are discussed, one intrinsic and the other associated with distributed circuit elements. Powerful new features have been added to the author's compex nonlinear least squares (CNLS) fitting program, and the results of a Monte Carlo simulation study of bias and statistical uncertainty in CNLS fitting of equivalent circuit data are discussed. The program now incorporates new variable weighting choices which can greatly minimize such bias. It also allows two unknown weighting parameters of the error variance model to be automatically estimated during the least squares fitting, thus best matching the weighting to the data and yielding most appropriate estimates of the parameters of the fitting model.