To overcome the problem of HIV-1 variability, candidate vaccine antigens have been designed to be composed of conserved elements of the HIV-1 proteome. Such candidate vaccines could be improved with a better understanding of both HIV-1 evolutionary constraints and the fitness cost of specific mutations. We evaluated the in vitro fitness cost of 23 mutations engineered in the HIV-1 subtype B Gag-p24 Center-of-Tree (COT) protein through fitness competition assays. While some mutations at conserved sites exacted a high fitness cost, as expected under the assumption that the most conserved residue confers the highest fitness, there was no overall strong relationship between sequence conservation and replicative capacity. By comparing sites that have evolved since the beginning of the epidemic to those that have remain unchanged, we found that sites that have evolved over time were more likely to correspond to HLA-associated sites and that their mutation had limited fitness costs. Our data showed no transcendent link between high conservation and high fitness cost, indicating that merely focusing on conserved segments of HIV-1 would not be sufficient for a successful vaccine strategy. Nonetheless, a subset of sites exacted a high fitness cost upon mutation--these sites have been under selective pressure to change since the beginning of the epidemic but have proved virtually nonmutable and could constitute preferred targets for vaccine design.