Mice, tissues, cells, and genetic material are provided that comprise a humanized heavy chain immunoglobulin locus, a humanized light chain locus that expresses a universal light chain, and a gene encoding an ADAM6 or ortholog or homolog or functional fragment thereof. Mice are provided that express humanized heavy chains comprising human variable domains, and that express humanized light chains comprising human variable domains wherein the light chains are derived from no more than one, or no more than two, light chain V and J or rearranged V/J sequences. Fertile male mice that express antibodies with universal light chains and humanized heavy chains are provided. Methods and compositions for making bispecific binding proteins are provided.