This manuscript revisits the assertion of Berthier et al. that competing fractional-element equivalent-circuit models of battery cells are indistinguishable in the presence of noise. Starting with Westerhoff’s general equivalent-circuit model (ECM) of 2016 and an idealized impedance spectrum of a lithium battery, a contemporary set of possible ECMs are chosen. Their distinguishability is investigated. Using the extended frequency range recommended by Mauracher & Karden in 1997 or Hasan & Scott in 2019, an approach is presented that permits selection of the appropriate model, even in the presence of noise. For the given frequency range, models with up to five elements or eight real parameters are studied. Fitting to measured data with straightforward numerical methods and choosing the most primitive appropriate sub-circuit is shown to reproduce the data. Typically a three-element, five-parameter ECM is shown to model real, measured data with precision comparable to individual sample error.