The variance of errors in the impedance spectra is evaluated from replicate measurements. The variance of residual deviations from the fit of equivalent circuit is calculated in the case of semi-replicate measurements. A model of variance, which describes departures of the variance from being proportional to the squared absolute value of admittance, is fitted to the evaluated variance. Weights inversely proportional to the variance model are used in the CNLS fitting of the impedance spectra. The variance model weights are compared with the modulus weights in the proposed procedure for elimination of outliers in which the residual deviations are compared with standard deviations estimated in accordance with the applied weighting scheme and the root-mean-square residual of the fit. It is shown that the estimates of model parameters, using the variance model weights, are less sensitive to random errors of measurements than those using modulus weights.