Many dominantly inherited disorders are caused by missense amino acid substitutions resulting from a single nucleotide exchange in the encoding gene. For these disorders, where proteins expressed from the mutant alleles are often pathogenic and present throughout life, gene silencing, through intervention at the mRNA level, holds promise as a therapeutic approach. We have used mutations that underlie the slow channel congenital myasthenic syndrome (SCCMS) as a model system to study allele-specific gene silencing of RNA transcripts by DNAzymes. We tested the ability of DNAzymes to give allele-specific cleavage for i) mutations that create cleavage sites, and ii) mutations located close to a DNAzyme cleavage site that create a potential mismatch in the binding arms. For both we demonstrate selective cleavage of mutant transcripts under simulated physiological conditions. For DNAzymes with binding arm mismatches the degree of selectivity for mutant over wild type may be enhanced by optimising the mismatch position as well as the binding arm length. The optimal sites for mismatches are 1.1 and 1.2 in arm I, and 16.2 in arm II. Asymmetric binding arm DNAzymes with a shorter arm I are more discriminative. Our results show it should be possible to apply DNAzyme-mediated cleavage of mutant alleles even when the mutant does not itself create a putative cleavage site. This therapeutic approach may be well suited to dominantly inherited disorders such as SCCMS, where loss of some wild type transcripts is unlikely to have pathogenic consequences.