Second RPA calculations with a Skyrme force are performed to describe both high- and low-lying excited states in 16O. The coupling between 1 particle-1 hole and 2 particle-2 hole as well as that between 2 particle-2 hole configurations are fully taken into account and the residual interaction is never neglected. For the rearrangement terms in the matrix elements beyond standard RPA two approximations are employed: they are either neglected or evaluated with the RPA procedure. A several-MeV shift of the strength distribution to lower energies is systematically found with respect to RPA distributions. A better description of the excitation energies of the low-lying 0+ and 2+ states is obtained with second RPA with respect to RPA.