In contrast to molecular rates for neutral mitochondrial sequences, rates for constrained sites (including nonsynonymous sites, D-loop, and RNA) in the mitochondrial genome are known to vary with the time frame used for their estimation. Here, we examined this issue for the nuclear genomes using single-nucleotide polymorphisms (SNPs) from six complete human genomes of individuals belonging to different populations. We observed a strong time-dependent distribution of nonsynonymous SNPs (nSNPs) in highly constrained genes. Typically, the proportion of young nSNPs specific to a single population was found to be up to three times higher than that of the ancient nSNPs shared between diverse human populations. In contrast, this trend disappeared, and a uniform distribution of young and old nSNPs was observed in genes under relaxed selective constraints. This suggests that because mutations in constrained genes are highly deleterious, they are removed over time, resulting in a relative overabundance of young nSNPs. In contrast, mutations in genes under relaxed constraints are nearly neutral, which leads to similar proportions of young and old SNPs. These results could be useful to researchers aiming to select appropriate genes or genomic regions for estimating evolutionary rates and species or population divergence times.