Using optical-optical double resonance and an ultrasensitive ionization detector, we have been able to extensively study a wide range of internuclear distances for the 5 (1) Sigma(g)(+) state of Na-2. Using a combination of spectroscopic data and the ab initio calculations, we have constructed a hybrid potential which has an outer well at shelf region. For this hybrid potential, there are 54 vibrational levels in the inner well (which all have been observed in this work) and 12 vibrational levels in the outer well (of which only the last level has been observed in this work). Above the potential barrier, 78 additional vibrational levels have been observed in this work. These spectroscopic data represent about 99.8% of the potential well depth.