The 3 1SIGMA(g)+ state of Na2 has been extensively studied using an optical-optical double resonance technique and a shielded cylindrical space-charge-limited ionization detector. A wide range of vibrational quantum numbers 0 less-than-or-equal-to v less-than-or-equal-to 141 was observed which covered over 99.9% of the potential well depth. A ''shelf'' on the potential energy curve was found near v = 23. A hybrid potential was constructed based on the Rydberg-Klein-Rees (RKR) potential curve and a local inverse perturbation approach (IPA) for the shelf region. For this potential, there is a shallow second local minimum approximately 5 cm-1 in depth at the shelf region. The long range energy also compares well with long range theory.