The stepwise three-step three-color laser population of the I-2(beta 1(g), v(beta), J(beta)) rovibronic states via the B0(u)(+), v(B), J(B) rovibronic states and rovibronic levels of the 1(u)(bb) and 0(g)(+) (bb) states mixed by hyperfine interaction is used for determination of rovibronic level energies of the weakly bound I-2(1(u)(bb)) state. Dunham coefficients of the state, Y-i0 (i=0-3), Y-i1 (i=0-2), Y-02 and Y-12 for the v(1u) = 1-5, 8, 10, 15 and J(1u) approximate to 9-87 ranges, the dissociation energy of the state, D-e, and equilibrium I-I distance, R-e, as well as the potential energy curve are determined. There are aperiodicities in the excitation spectrum corresponding to the beta, v(beta) = 23, J(beta) <- 1(u)(bb), v(1u) = 4, 5, J(1u) progressions in the I-2 + Rg = He, Ar mixture, namely, a great number of lines which do not coincide with the R or P line progressions. Their positions conflict with the Delta J-even selection rule. Furthermore, they do not correspond to the Delta J-odd progression.