New ro-vibrational structures of cold Cs2 in the 0u(+) state near the asymptote 6S1/2 + 6P1/2 are resolved. The variation of the rotational constants shows that the related energy spectra are strongly perturbed. An analysis of new data along with the empirical and theoretical information available from other sources is performed. For this purpose the model of spin-orbit coupling of the Hund's case (a) states A(1)Σu(+)∼b(3)Πu proposed by Bai et al. [Phys. Rev. A 83, 032514 (2011)] is extrapolated to the dissociation limit, and the parameters of the extrapolation are fitted from the near-dissociation experimental data.