Public responses where identical T cell receptors (TCRs) are clonally dominant and shared between different individuals are a common characteristic of CD8⁺ T cell-mediated immunity. Focusing on TCR sharing, we analyzed ≈3,400 TCR β chains (TCRβs) from mouse CD8⁺ T cells responding to the influenza A virus D^bNP₃₆₆ and D^bPA₂₂₄ epitopes. Both the “public” D^bNP₃₆₆-specific and “private” D^bPA₂₂₄-specific TCR repertoires contain a high proportion (≈36%) of shared TCRβs, although the numbers of mice sharing TCRβs in each repertoire varies greatly. Sharing of both the TCRβ amino acid and TCRβ nucleotide sequence was negatively correlated with the prevalence of random nucleotide additions in the sequence. However, the extent of TCRβ amino acid sequence sharing among mice was strongly correlated with the level of diversity in the encoding nucleotide sequences, suggesting that a key feature of public TCRs is that they can be made in a variety of ways. Using a computer simulation of random V(D)J recombination, we estimated the relative production frequencies and variety of production mechanisms for TCRβ sequences and found strong correlations with the sharing of both TCRβ amino acid sequences and TCRβ nucleotide sequences. The overall conclusion is that “convergent recombination,” rather than a bias in recombination or subsequent selection, provides the mechanistic basis for TCR sharing between individuals responding to identical peptide plus MHC class I glycoprotein complexes.