Gene-drive systems developed in several organisms result in super-Mendelian inheritance of transgenic insertions. Here, we generalize this "active genetic" approach to preferentially transmit allelic variants (allelic-drive) resulting from only a single or a few nucleotide alterations. We test two configurations for allelic-drive: one, copy-cutting, in which a non-preferred allele is selectively targeted for Cas9/guide RNA (gRNA) cleavage, and a more general approach, copy-grafting, that permits selective inheritance of a desired allele located in close proximity to the gRNA cut site. We also characterize a phenomenon we refer to as lethal-mosaicism that dominantly eliminates NHEJ-induced mutations and favors inheritance of functional cleavage-resistant alleles. These two efficient allelic-drive methods, enhanced by lethal mosaicism and a trans-generational drive process we refer to as "shadow-drive", have broad practical applications in improving health and agriculture and greatly extend the active genetics toolbox.