The present invention provides substituted humanized, chimeric or human anti-CD20 antibodies or antigen binding fragments thereof and bispecific antibodies or fusion proteins comprising the substituted antibodies or antigen binding fragments thereof. The antibodies, fusion proteins or fragments are useful for treatment of B-cell disorders, such as B-cell malignancies and autoimmune diseases, as well as GVHD, organ transplant rejection, and hemolytic anemia and cryoglobulinemia. Amino acid substitutions, particularly substitution of an aspartate residue at Kabat position 101 of CDR3 VH (CDRH3), result in improved therapeutic properties, such as decreased dissociation rates, improved CDC activity, improved apoptosis, improved B-cell depletion and improved therapeutic efficacy at very low dosages. Veltuzumab, a humanized anti-CD20 antibody that incorporates such sequence variations, exhibits improved therapeutic efficacy compared to similar antibodies of different CDRH3 sequence, allowing therapeutic effect at dosages as low as 200 mg or less, more preferably 100 mg or less, more preferably 80 mg or less, more preferably 50 mg or less, most preferably 30 mg or less of naked antibody when administered i.v. or s.c.