Certain Major Histocompatibility-I (MHC-I) types are associated with superior immune containment of HIV-1 infection by CD8⁺ cytotoxic T lymphocytes (CTLs), but the mechanisms mediating this containment are difficult to elucidate in vivo. Here we provide controlled assessments of fitness landscapes and CTL-imposed constraints for immunodominant epitopes presented by two protective (B*57 and B*27) and one non-protective (A*02) MHC-I types. Libraries of HIV-1 with saturation mutagenesis of CTL epitopes are propagated with and without CTL selective pressure to define the fitness landscapes for epitope mutation and escape from CTLs via deep sequencing. Immunodominant B*57- and B*27- present epitopes are highly limited in options for fit mutations, with most viable variants recognizable by CTLs, whereas an immunodominant A*02 epitope-presented is highly permissive for mutation, with many options for CTL evasion without loss of viability. Generally, options for evasion overlap considerably between CTL clones despite highly distinct T cell receptors. Finally, patterns of variant recognition suggest population-wide CTL selection for the A*02-presented epitope. Overall, these findings indicate that these protective MHC-I types yield CTL targeting of highly constrained epitopes, and underscore the importance of blocking public escape pathways for CTL-based interventions against HIV-1.