We report an accurate inverted perturbation approach (IPA) potential energy curve for the "shelf" F (1)Sigma (+)(g) state in Li-2 which reproduces positions of the experimental energy levels available in the literature for all three isotopomers Li-7(2), (LiLi)-Li-6-Li-7, and Li-6(2) with a standard deviation of 0.11 cm(-1). Our analysis significantly improves the shape of the recently reported Rydberg-Klein-Rees (RKR) potential curve of the F (1)Sigma (+)(g) state [Antonova , J. Chem. Phys. 112, 7080 (2000)] and provides evidence for the existence of a shallow minimum in the shelf region. Using our IPA potential curve we were able to localize and identify some local perturbations in the spectra, as well as to correct the assignment of several spectral lines previously observed experimentally.