A method for generating a human immunoglobulin heavy and/or kappa light chain variable region sequence comprising the steps of: (a) immunizing a genetically modified mouse with an antigen, wherein the genetically modified mouse generates antibodies when immunized with the antigen, and wherein the genetically modified mouse has a germline genome that comprises: (i) two human immunoglobulin Vκ gene segments and five human immunoglobulin Jκ gene segments operably linked to a mouse or rat immunoglobulin light chain constant region sequence, wherein the two human immunoglobulin Vκ gene segments are a human Vκ1-39 and a human Vκ3-20, and the five human immunoglobulin Jκ gene segments are human Jκ1, human Jκ2, human Jκ3, human Jκ4, and human Jκ5; and (ii) one or more unrearranged human immunoglobulin V H gene segments, one or more unrearranged human immunoglobulin D H gene segments, and one or more unrearranged human immunoglobulin J H gene segments operably linked to a mouse immunoglobulin heavy chain constant region sequence; wherein the unrearranged human heavy chain gene segments and unrearranged human kappa light chain gene segments of the mouse are capable of rearranging and encoding human heavy chain variable domains and human kappa light chain variable domains, respectively, of an antibody, and wherein the mouse does not comprise an endogenous Vκ gene segment that is capable of rearranging to form a light chain variable region sequence, and (b) determining a human immunoglobulin heavy and/or kappa light chain variable region sequence that encodes a human immunoglobulin heavy or light chain variable domain, respectively, of an antibody that specifically binds the antigen and that was generated by the genetically modified mouse. (a) immunizing a genetically modified mouse with an antigen, wherein the genetically modified mouse generates antibodies when immunized with the antigen, and wherein the genetically modified mouse has a germline genome that comprises: (i) two human immunoglobulin Vκ gene segments and five human immunoglobulin Jκ gene segments operably linked to a mouse or rat immunoglobulin light chain constant region sequence, wherein the two human immunoglobulin Vκ gene segments are a human Vκ1-39 and a human Vκ3-20, and the five human immunoglobulin Jκ gene segments are human Jκ1, human Jκ2, human Jκ3, human Jκ4, and human Jκ5; and (ii) one or more unrearranged human immunoglobulin V H gene segments, one or more unrearranged human immunoglobulin D H gene segments, and one or more unrearranged human immunoglobulin J H gene segments operably linked to a mouse immunoglobulin heavy chain constant region sequence; wherein the unrearranged human heavy chain gene segments and unrearranged human kappa light chain gene segments of the mouse are capable of rearranging and encoding human heavy chain variable domains and human kappa light chain variable domains, respectively, of an antibody, and wherein the mouse does not comprise an endogenous Vκ gene segment that is capable of rearranging to form a light chain variable region sequence, and (i) two human immunoglobulin Vκ gene segments and five human immunoglobulin Jκ gene segments operably linked to a mouse or rat immunoglobulin light chain constant region sequence, wherein the two human immunoglobulin Vκ gene segments are a human Vκ1-39 and a human Vκ3-20, and the five human immunoglobulin Jκ gene segments are human Jκ1, human Jκ2, human Jκ3, human Jκ4, and human Jκ5; and (ii) one or more unrearranged human immunoglobulin V H gene segments, one or more unrearranged human immunoglobulin D H gene segments, and one or more unrearranged human immunoglobulin J H gene segments operably linked to a mouse immunoglobulin heavy chain constant region sequence; (b) determining a human immunoglobulin heavy and/or kappa light chain variable region sequence that encodes a human immunoglobulin heavy or light chain variable domain, respectively, of an antibody that specifically binds the antigen and that was generated by the genetically modified mouse.