Abstract: Herein is reported a method for increasing the (avid-)binding specificity of a bispecific antibody comprising a first mammalian or mammalianized binding site specifically binding to a first (cell-surface) antigen and a second binding site specifically binding to a second (cell-surface) antigen, wherein the first mammalian or mammalianized binding site is at least a pair of an immunoglobulin light chain variable domain and immunoglobulin heavy chain variable domain, by decreasing the binding affinity of the mammalian or mammalianized binding site to its antigen by mutating in the first mammalian or mammalianized binding site at least one amino acid residue at a position in the CDRs of the light chain variable domain or in the CDR1 or CDR2 of the heavy chain variable domain or in the two framework positions directly preceding the CDR3 in the heavy chain variable domain to an amino acid residue present at said position in a germline immunoglobulin amino acid sequence of the same mammalian species as that of the