Bispecific antibodies (bsAbs) with avidity-enhanced specificity can be used to address target cells with increased specificity, ideally binding efficiently to cells that express two cognate antigens, yet not to cells that express only one of those. Building blocks required to generate such bsAbs are binders that recognize the two antigens with high specificity yet with various (including very low monovalent) affinities. The herein described 'back-to-germline' (B2G) procedure defines such derivatives. It converts parent antibodies with high specificity to derivatives that retain specificity but modulate affinity. The approach defines mutations to be introduced into antibody complementarity-determining regions (CDRs) regions without requiring structures of antibody-antigen complexes. Instead, it reverses the B-cell maturation process that increases affinities, with preference on CDR residues with high antigen contact probability. Placing germline residues at those positions generates VH and VL domains and Fv-combinations thereof that retain specificities but are 'de-matured' to different degrees. De-maturation influences on-rates and off-rates, and can produce entities with extremely low affinity for which binding can only be detected in bivalent formats. A comparison with alanine replacement in CDRs (so far, the most frequently applied technology) indicates that B2G may be more reliable/predictable without introduction of stickiness or poly-reactivity. The applicability for generating sets of affinity-modulated monospecific variants is exemplarily shown for antibodies that bind CD138, Her2/neu, and EGFR.