A genetically modified mouse is provided, wherein the mouse expresses an immunoglobulin light chain repertoire characterized by a limited number of light chain variable domains. Mice are provided that express just one or a few immunoglobulin light chain variable domains from a limited repertoire in their germline. Methods for making light chain variable regions in mice, including human light chain variable regions, are provided. Methods for making human variable regions suitable for use in multispecific binding proteins, e.g., bispecific antibodies, are provided.