The Fletcher's proposition [S Fletcher. Electrochemistry Communications 3 (2001) 692-696] to represent a three-terminal electrochemical cell by its two-terminal electrical equivalent for the purpose of the analysis of its electrical responses helps significantly to elucidate peculiarities of the electrochemical impedance (EI) such as inductive or capacitive artifacts. The Fletcher's two-terminal equivalent cell of 3rd order appears however to be redundant as including more circuit elements then necessary to represent the 2nd older impedance of the electrochemical cell. As the alternative to this we recommend two equivalent circuits of 2nd order, both simpler then the original Fletcher's circuit and both better candidates to play the role of the canonical electrical model. Transformation front three-terminal to two-terminal circuit done here with Mathematical (R) program appeared relatively simple and it was also possible to relax Fletcher's restraint of representing the working electrode by single resistance Instead, we used two-terminal electrical models with the working electrode represented by series resistance, double layer capacitance and charge transfer resistance El spectra of such extended configuration also present capacitive and inductive artifacts referred to by Fletcher in his model. These artifacts do depend on the impedance of the working electrode. (C) 2009 Elsevier Ltd. All rights reserved