Ro-vibrational term values of the 3 1 Σ g + state of ^85,85Rb₂ and ^85,87Rb₂ and resolved fluorescence spectra to the A 1 Σ u + state are recorded following optical-optical double resonance excitation. The experimental data are heavily perturbed, and as a result, the standard analysis based on Dunham series representation of the energy levels fails. The analysis is done via modeling the adiabatic potential function with the Rydberg-Klein-Rees potential constructed from the generalized smoothing spline interpolation of the vibrational energies G_v and rotational constants B_v.