Following the poor clinical results of antiangiogenic drugs, particularly when applied in isolation, tumour biologists and clinicians are now turning to combinations of therapies in order to obtain better results. One of these involves vessel normalisation strategies. In this paper, we investigate the effects on tumour growth of combinations of antiangiogenic and standard cytotoxic drugs, taking into account vessel normalisation. An existing multiscale framework is extended to include new elements such as tumour-induced vessel dematuration. Detailed simulations of our multiscale framework allow us to suggest one possible mechanism for the observed vessel normalisation-induced improvement in the efficacy of cytotoxic drugs: vessel dematuration produces extensive regions occupied by quiescent (oxygen-starved) cells which the cytotoxic drug fails to kill. Vessel normalisation reduces the size of these regions, thereby allowing the chemotherapeutic agent to act on a greater number of cells.