Provided herein are methods for generating conjugated immunoglobulins, the method comprising: decapping a cysteine at amino acid position 80 (“Cys80”) in a light chain variable region of an immunoglobulin, wherein the immunoglobulin comprises a heavy chain variable region and the light chain variable region; and conjugating a thiol-reactive compound to the Cys80, wherein the thiol-reactive compound comprises a thiol-reactive group. Antigen-binding molecules and methods for generating the same, immunoglobulins as well as nucleic acid molecules encoding the immunoglobulins and host cells comprising the nucleic acid molecules, conjugated immunoglobulins, and light chain variable regions for use in a conjugated immunoglobulin are also provided.