HLA-A*6801 exhibits several unusual features. First, it is known to bind weakly to CD8 due to the presence of an A245V substitution in the α3 domain. Second, it is able to accommodate unusually long peptides as a result of peptide ‘kinking’ in the binding groove. Third, CD8+ cytotoxic T lymphocytes that recognise HLA-A*6801-restricted antigens can tolerate substantial changes in the peptide sequence without apparent loss of recognition. In addition, it has been suggested that HLA-A68-restricted TCR might bind with higher affinity than other TCR due to their selection in the presence of a decreased contribution from CD8. Here we (1) examine monoclonal T cell recognition of an HLA-A*6801-restricted HIV-1 Tat-derived 11-amino acid peptide (ITKGLGISYGR) and natural variant sequences thereof; (2) measure the affinity and kinetics of a TCR/pHLA-A68 interaction biophysically for the first time, showing that equilibrium binding occurs within the range previously determined for non-HLA-A68-restricted TCR (KD approx. 7 μM); and (3) show that “normalization” of the non-canonical HLA-A*6801 CD8-binding domain enhances recognition of agonist peptides without inducing non-specific activation. This latter effect may provide a fundamental new mechanism with which to enhance T cell immunity to specific antigens.