Genetically modified mice and methods for making and using them are provided, wherein the mice comprise a replacement of all or substantially all immunoglobulin heavy chain V gene segments, D gene segments, and J gene segments with at least one light chain V gene segment and at least one light chain J gene segment. Mice that make binding proteins that comprise a light chain variable domain operably linked to a heavy chain constant region are provided. Binding proteins that contain an immunoglobulin light chain variable domain, including a somatically hypermutated light chain variable domain, fused with a heavy chain constant region, are provided. Modified cells, embryos, and mice that encode sequences for making the binding proteins are provided.
