The extent of allelic exclusion in Ig genes is very high, although not absolute. Thus far, it has not been clearly established whether rapid selection of the developing B cell as soon as it has achieved the first productively rearranged, functional heavy chain is the only mechanism responsible for allelic exclusion. Our computational models of Ag receptor gene rearrangement in B lymphocytes are hereby extended to calculate the expected fractions of heavy chain allelically included newly generated B cells as a function of the probability of heavy chain pairing with the surrogate light chain, and the probability that the cell would test this pairing immediately after the first rearrangement. The expected fractions for most values of these probabilities significantly exceed the levels of allelic inclusion in peripheral B cells, implying that in most cases productive rearrangement and subsequent cell surface expression of one allele of the heavy chain gene probably leads to prevention of rearrangement completion on the other allele, and that additional mechanisms, such as peripheral selection disfavoring cells with two productively rearranged heavy chain genes, may also play a role. Furthermore, we revisit light chain allelic exclusion by utilizing the first (to our knowledge) computational model which addresses and enumerates B cells maturing with two productively rearranged κ light chain genes. We show that, assuming that there are no selection mechanisms responsible for abolishing cells expressing two light chains, the repertoire of newly generated B lymphocytes exiting the bone marrow must contain a significant fraction of such κ double-productive B cells.