The recently proposed Fully-Renormalized QRPA (FR-QRPA), which fullfils the Ikeda sum rule (ISR) exactly, is applied to the two-neutrino double beta decay of 76 Ge, 82 Se, 100 Mo, 116 Cd, 128 Te and 130 Xe. The results obtained are compared with those of other approaches, standard QRPA and self-consistent QRPA (SCQRPA). The similarities and the differences among the methods are discussed. The influence of the restoration of the Ikeda sum rule on the 2νββ-decay amplitude is analyzed.21.60.Jz, 23.40.Hc