The present invention is based, at least in part, on the discovery that strategic modifications of non-human donor antibody CDR residue(s) can be used to humanize antibodies. Such modifications modulate the 3D structural fit between donor antibody CDRs and human acceptor antibody framework regions that comprise the variable domains of a CDR-grafted antibody. Whereas prior art methods of humanization have relied on making framework substitutions (in which selected human framework residues are backmutated to the corresponding amino acid residue present in the non-human donor antibody), the instant invention is based, at least in part, on a method of humanizing antibodies in which selected CDR residues, and optionally adjacent FR residues, are changed in order to accommodate differences in FR amino acid sequences between donor and acceptor antibodies.