How the vast majority of B cells express only one of the two alleles at their immunoglobulin loci remains a biological puzzle. Here, in mice reconstituted with a single haematopoietic stem cell, we demonstrate that each of the two immunoglobulin heavy chain (Igh) alleles has a similar probability to be the first to undergo V(H) to DJ(H) rearrangement. We also observe this similar probability in clones from multipotent and common lymphoid precursors. The extreme biases in the expression of the alleles that we find in more differentiated subsets are mostly due to constraints imposed by early rearrangements. Our data demonstrate that each of the two Igh alleles in a B cell behaves independently of the other, up to the moment when a successful rearrangement in one allele triggers a feedback mechanism that prevents further recombination.