Methods are disclosed for correcting a mutant allele of a gene of interest in a primate cell. The methods include a) introducing a non-naturally occurring targeted nuclease and site-specific nucleotide-binding guide that act together to introduce double-stranded breaks in the mutant allele into the primate cell, wherein: i) the primate cell is undergoing mitotic cell division; ii) the primate cell comprises a genome that is heterozygous for the mutant allele, such that the genome comprises one copy of the mutant allele and one copy of a wild-type allele; iii) single-stranded oligonucleotides homologous to the wild-type allele are not introduced into the primate cell. The methods also include b) allowing the primate cell to activate homology-directed repair of the double-stranded DNA breaks in the mutant allele, thereby correcting the mutant allele using the normal wild-type allele as a repair template and producing a primate cell that is homozygous for the wild-type allele. The primate cell can be a one-cell embryo and/or a human cell.