The invention provides bispecific antibodies with selective cytotoxicity against malignant B-cells. The bispecific antibodies bind to an effector cell antigen and to a 28/32 kDa heterodimeric protein on the surface of malignant B-cells. The invention also includes the monospecific components of the bispecific antibodies, humanized versions thereof, and humanized bispecific antibodies. The invention further provides therapeutic and diagnostic methods employing these antibodies.