The invention provides modified antibodies directed against GD2 that have diminished complement fixation relative to antibody-dependent, cell-mediated cytotoxicity, which is maintained. The modified antibodies of the invention may be used in the treatment of tumors such as neuroblastoma, glioblastoma, melanoma, small-cell lung carcinoma, B-cell lymphoma, renal carcinoma, retinoblastoma, and other cancers of neuroectodermal origin.