Mitochondrial genomes are by definition compact and structurally stable over aeons. This generalized perception results from a vertebrate-centric vision, as very few types of mtDNA rearrangements have been described in vertebrates. By combining a panel of sequencing approaches, including short- and long-reads, we show that species from a group of illusive marine teleosts, the deep-sea hatchetfish (Stomiiforms: Sternoptychidae), display a myriad of new mtDNA structural arrangements. We show a never reported inversion of the coding direction of protein-coding genes (PGG) coupled with a strand asymmetry nucleotide composition reversal directly related to the strand location of the Control Region (which includes the heavy strand replication origin). An analysis of the 4-fold redundant sites of the PCGs, in thousands of vertebrate mtDNAs, revealed the rarity of this phenomenon, only found in 9 fish species, five of which being deep-sea hatchetfish. Curiously, in Antarctic notothenioid fishes (Trematominae), where a single PCG inversion (the only other record in fish) is coupled with the inversion of the Control Region, the standard asymmetry is disrupted for the remaining PCG but not yet reversed, suggesting a transitory state in this species mtDNA. Together, our findings suggest that a relaxation of the classic vertebrate mitochondrial structural stasis, observed in Sternoptychidae and Trematominae, promotes disruption of the natural balance of asymmetry of the mtDNA. Thus, supporting the long-lasting hypothesis that replication is the main molecular mechanism promoting the strand-specific compositional bias of this unique and indispensable molecule.