Antibody gene rearrangements can continue despite the presence of productively rearranged heavy and light chain genes. The function(s) of these ongoing antibody gene rearrangements is unknown, although it has been proposed that continued rearrangement allows B cells with defective or autoreactive receptors to edit those receptors. To study the role of editing in rescuing B cells with dysfunctional receptors, animals with simplified immunoglobulin light chain genes were constructed and characterized: $\kappa$ deficient animals were used to assess the extent of ongoing rearrangement of $\kappa$ and $\lambda$ light chains. Animals with only one functional $\kappa$ L-chain allele (kdel/wt) were used to study editing by successive $\kappa$ L-chain rearrangement (leapfrogging). Consistent with leapfrogging, a bias towards distal J$\kappa$ rearrangements was observed in kdel/wt B cells. Southern blotting and PCR analysis confirmed the presence of multiple $\kappa$ rearrangements in some kdel/wt clones. To study editing of $\lambda$ light chains, rearrangements were characterized in kde/kdel mice. Some kdel/kdel B cells had multiple, productive $\lambda$ rearrangements, suggestive of editing by light chain competition for heavy chain pairing.