The connection between two of the most frequently used mathematical models to fit the soft breakdown I-V characteristic in MOS devices was investigated. First, we show that our experimental data is well represented by the monomial power-law model and we extract its parameters by means of an auxiliary operator that involves numerical integration of the I-V curve. Next, we consider the co-tunneling conduction model, which represents the current by a polynomial expression with only odd-order terms and positive coefficients. The best fit of our experimental data to odd-order polynomials yields some negative coefficients, which is contrary to its physical foundations. Finally, in an attempt to conciliate both representations, we have approximated the power-law model to a polynomial with only odd-order terms and arbitrary coefficients and again we have found that is not possible to obtain all positive coefficients.