Non-human animals, tissues, cells, and genetic material are provided that comprise a modification of an endogenous non-human heavy chain immunoglobulin sequence and that comprise an ADAM6 activity functional in a rodent (e.g., a mouse), wherein the non-human animals rearrange human immunoglobulin light chain gene segments in the context of heavy chain constant regions and express immunoglobulin-like molecules comprising human immunoglobulin light chain variable domains fused to heavy chain constant domains that are cognate with human immunoglobulin light chain variable domains fused to light chain constant domains.