We fit the S-1(0) Lambda Lambda interaction in the nuclear medium to the masses of the experimentally known double-Lambda hypernuclei: He-6(Lambda Lambda), Be-10(Lambda Lambda) and B-13(Lambda Lambda). We derive this effective interaction from OBE Julich Lambda Lambda-type potentials and using both Hartree-Fock and variational approaches. We find that the inclusion of nn correlations in the variational scheme leads to significant differences and a better understanding of the dynamical features of the system. We investigate the sensitivity of the binding energies and the mesonic decay widths of the above double-Lambda hypernuclei to the omega Lambda Lambda coupling and the form factor at the sigma Lambda Lambda vortex, We also use this effective interaction to predict binding energies and pionic decay widths of heavier double-Lambda hypernuclei, not discovered yet. Finally, we discard the existence of S-1(0) Lambda Lambda bound states provided the Lambda Lambda-Xi N coupling can be neglected.