Anionic states of Li-3 were studied theoretically using a full-valence complete active space (CAS) self-consistent field (SCF) approach to explore their potential energy surfaces followed by quadratic configuration interaction with single, double, and approximate triple excitations calculations to more accurately determine relative energies and electron detachment energies. In addition to the known (1) Sigma(g)(+) state, one triplet ((3)A’(2)) and two quintet (5A"(1) and (5)A’(2)) states were found to be relatively low lying and electronically and geometrically stable in D-3h geometries. All of these states remain electronically stable in C-2 nu and D-infinity h geometries. Hence, they are amenable to photoelectron spectroscopy detection. Preliminary CAS SCF results for the valence isoelectronic Na-3(-) are also reported.