  We describe a modification of the inverted perturbation approach method
allowing to construct physically sensible potential energy curves for
electronic states of diatomic molecules even when some parts of the potential
are not adequately characterized by the experimental data. The method is based
on a simple regularization procedure, imposing an additional constraint on the
constructed potential curve. In the present work it is applied to the double
minimum 4$^1\Sigma^{+}_{\mathrm u}$ state of Na$_2$, observed experimentally by
polarization labeling spectroscopy technique.
