The sensitivity of the self-consistent values for the position and width of the $\rho$ meson, as given by the twopole method of Balázs, to the value of the matching parameter ${\nu }_F$, is studied. We find that, while self-consistent solutions exist for all values of ${\nu }_F$ studied, the resonance parameters ${\nu }_r$ and $\Gamma$ vary by roughly factors of 2 and 1.4, respectively, as ${\nu }_F$ is varied over a reasonable range. By requiring that the second derivatives of the two forms of the amplitude match or, equivalently, by requiring that there be reasonable agreement between the two forms of the amplitude and of the first derivative over a range of values of ${\nu }_F$, and not just at the matching point, we are able to give a plausible argument for which value of ${\nu }_F$ should be selected. The resonance position corresponding to this value of ${\nu }_F$ is in somewhat better agreement with experiment than that obtained with the value of ${\nu }_F$ used in Balázs's original paper, while the width obtained is slightly wider and hence in worse agreement.

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