We investigate the interplay of the nuclear and Coulomb interaction in the fragmentation of relativistic Li-11 projectiles incident on several targets. The Li-11 nucleus is assumed to have a cluster-like structure, with a (bound) di-neutron system coupled to a Li-9 core in an s-state. The obtained nuclear cross sections show marked differences with the "experimental" data. Taking the calculated nuclear contribution at face value results in a Coulomb dissociation cross section, sigma-C, which is well reproduced by recent modified-RPA calculation. The pure cluster model then overestimates sigma-C by about 20%.