The contention made by Berthier et al. - that competing fractional-element equivalent- circuit models of battery cells are indistinguishable in the presence of noise - is revisited in this work. A set of six equivalent circuit models (ECMs) were chosen as a subset of West- erhoff’s generalised ECM from 2016. These six ECMs had increasing complexity, and gave a simulated output similar to that of an idealised Lithium battery impedance spec- trum. By extending the frequency range of Berthier, using methods suggested by both Mauracher & Karden, and Hasan & Scott, sets of simulated electrochemical impedance spectra (EIS) are generated. A Nelder-Mead based optimisation method, which em- ploys multiple restarts, is used to fit each ECM to the sets simulated data. The data was produced with 0%, 1%, 3% and 5% noise. The optimisations showed that all six ECMs were distinguishable at 0% noise, but as the noise increased - distinguishability is lost. Typically a 4-element ECM is shown to model the simulated data with preci- sion which is comparable to the error in the data. When optimising the ECMs against measured data (measured with an Egilent 66332A, E5270 and a Keithley 2460A) from INR and NCA batteries, it is seen that the 3-element ECMs are an adequate model. However there is some variation between the two battery chemistries. Battery ageing and the measurement system used also contribute to variation in which ECM models the data best. Further work on this project should include repeating this fitting method on different battery chemistries, and collating and fitting ECMs to a battery which is measured at different points as it ages.