On the basis of a new, highly accurate potential energy hypersurface for th
e lowest triplet state of H-3(,)+ (3)Sigma (+)(u), the bound ro-vibronic st
ates are calculated for J less than or equal to 5. Since the potential has
very shallow minima, those states exist only up to single vibrational excit
ation. The symmetry properties of the re-vibrational states are investigate
d. Further, it is demonstrated that the first excited triplet state, which
intersects conically with the (3)Sigma (+)(u) state, has no effect on the r
eported re-vibrational energies.