It was shown in a previous paper that the distortion induced by local inhomogeneities of equivalent-circuit model parameters in EIS data could be treated in terms of the average, the deviation and higher moments of the parameter distribution. Further refinements of the method are discussed. Evidence is provided that, at a frequently applied equivalent circuit, the lognormal distribution of the time constants can cause constant-phase behaviour in the EIS diagrams over a frequency range of several orders of magnitude.