Mitoviruses replicate in mitochondria of their host fungi. They have small RNA genomes that encompass a single ORF encoding the viral RdRp. Since UGA codons encode Trp in fungal mitochondria, the RdRp ORF of a typical mitovirus includes multiple UGA codons. In some mitoviruses, however, the ORF has no such codons, suggesting that these particular viruses may be under selective pressure to exclude them. In this report, new evidence is presented that host fungi whose mitoviruses have no or few UGA codons are distinctive in also having no or few UGA codons in their core mitochondrial genes. Thus, the relative exclusion of such codons in a subset of mitoviruses appears to reflect most fundamentally that UGA(Trp) is a rare mitochondrial codon in their particular hosts. The fact that UGA(Trp) is a rare mitochondrial codon in many fungi appears not to have been widely discussed to date.