A method is presented of avoiding ambiguities in linear Kramers-Kronig validity tests due to under- and over-fitting. It is based on the observation that the parameters of the equivalent circuit model to be fitted start degenerating as soon as the model order chosen is too high and over-fitting is taking place. Hence, a measure of the degree of degeneration is introduced and from this a criterion is developed with which over-fitting can be easily detected. Furthermore, it is shown, how the developed criterion can be used to automatically find an appropriate model order for any given impedance spectrum. Hereby, unambiguous test results are obtained irrespective of the specific expertise of the operator. Due to its ease of use the so improved test can serve as a quick standard test revealing defectiveness of measured impedance spectra. The validity of the proposed strategy is demonstrated in simulations as well as on measurements of a commercial Lithium-Ion battery.