A method of producing a nucleic acid encoding a human lambda light chain variable domain and/or a nucleic acid encoding a human heavy chain variable domain comprising the steps of: (a) immunizing a genetically modified rodent with an antigen, wherein the genetically modified rodent has a germline genome that comprises: (i) one or more human Vλ gene segments; (ii) one or more human Jλ gene segments; (iii) one or more human Cλ gene segments; (iv) one or more rodent immunoglobulin λ light chain enhancers (Eλ); (v) three human Eλs; and (vi) a rodent Cλ gene segment, wherein (i)-(vi) are at an endogenous immunoglobulin λ light chain locus; wherein (i) and (ii) are capable of rearranging to form rearranged human λ variable region genes that are expressed in conjunction with constant region gene segments of (iii) as λ light chains of antigen binding proteins, and wherein (i) and (ii) are also capable of rearranging to form rearranged human λ variable region genes that are expressed in conjunction with the rodent Cλ gene segment of (vi) as λ light chains of antigen binding proteins; and (vii) an engineered heavy chain locus comprising an insertion of one or more human V H gene segments, one or more human D H gene segments, and one or more human J H gene segments capable of rearranging to form rearranged human heavy chain variable region genes that are expressed in conjunction with a rodent immunoglobulin heavy chain constant region gene segment; (b) maintaining the rodent under conditions sufficient that the rodent produces an immune response to the antigen; and (c) recovering the nucleic acid encoding the human lambda light chain variable domain and/or the nucleic acid encoding the human heavy chain variable domain from the rodent, or a cell from the rodent. (a) immunizing a genetically modified rodent with an antigen, wherein the genetically modified rodent has a germline genome that comprises: (i) one or more human Vλ gene segments; (ii) one or more human Jλ gene segments; (iii) one or more human Cλ gene segments; (iv) one or more rodent immunoglobulin λ light chain enhancers (Eλ); (v) three human Eλs; and (vi) a rodent Cλ gene segment, wherein (i)-(vi) are at an endogenous immunoglobulin λ light chain locus; wherein (i) and (ii) are capable of rearranging to form rearranged human λ variable region genes that are expressed in conjunction with constant region gene segments of (iii) as λ light chains of antigen binding proteins, and wherein (i) and (ii) are also capable of rearranging to form rearranged human λ variable region genes that are expressed in conjunction with the rodent Cλ gene segment of (vi) as λ light chains of antigen binding proteins; and (vii) an engineered heavy chain locus comprising an insertion of one or more human V H gene segments, one or more human D H gene segments, and one or more human J H gene segments capable of rearranging to form rearranged human heavy chain variable region genes that are expressed in conjunction with a rodent immunoglobulin heavy chain constant region gene segment; (i) one or more human Vλ gene segments; (ii) one or more human Jλ gene segments; (iii) one or more human Cλ gene segments; (iv) one or more rodent immunoglobulin λ light chain enhancers (Eλ); (v) three human Eλs; and (vi) a rodent Cλ gene segment, wherein (i)-(vi) are at an endogenous immunoglobulin λ light chain locus; wherein (i) and (ii) are capable of rearranging to form rearranged human λ variable region genes that are expressed in conjunction with constant region gene segments of (iii) as λ light chains of antigen binding proteins, and wherein (i) and (ii) are also capable of rearranging to form rearranged human λ variable region genes that are expressed in conjunction with the rodent Cλ gene segment of (vi) as λ light chains of antigen binding proteins; and wherein (i)-(vi) are at an endogenous immunoglobulin λ light chain locus; wherein (i) and (ii) are capable of rearranging to form rearranged human λ variable region genes that are expressed in conjunction with constant region gene segments of (iii) as λ light chains of antigen binding proteins, and wherein (i) and (ii) are also capable of rearranging to form rearranged human λ variable region genes that are expressed in conjunction with the rodent Cλ gene segment of (vi) as λ light chains of antigen binding proteins; and (vii) an engineered heavy chain locus comprising an insertion of one or more human V H gene segments, one or more human D H gene segments, and one or more human J H gene segments capable of rearranging to form rearranged human heavy chain variable region genes that are expressed in conjunction with a rodent immunoglobulin heavy chain constant region gene segment; (b) maintaining the rodent under conditions sufficient that the rodent produces an immune response to the antigen; and (c) recovering the nucleic acid encoding the human lambda light chain variable domain and/or the nucleic acid encoding the human heavy chain variable domain from the rodent, or a cell from the rodent.