A method for quickly assessing the relative proportion of compact myocardium in the ventricle of teleosts is introduced and used in juvenile Pacific tarpon Megalops cyprinoides, a member of the only air-breathing elopomorph teleost genus. The proportion of compact myocardium increased with body mass, reaching up to 60% of the ventricular mass. The finding for tarpon was a surprising discovery since recent literature has suggested that air breathing evolved primarily as means of supplying oxygen to the fish heart during activity. The present data, which represent the first quantitative assessment of the compact myocardium for any air-breathing fish, suggest that myocardial oxygen supply in the tarpon is supplemented by the coronary circulation associated with compact myocardium during exercise, while air breathing is important during aquatic hypoxia. Compact myocardium was also measured as a point of reference in an extant representative from a more ancient fish lineage than the elopomorphs, the water-breathing spiny dogfish Squalus acanthias and found to be only 9% of ventricular mass. In conclusion, the presence of a coronary circulation in extant elasmobranchs may mean that the coronary circulation evolved well before air breathing in fishes and, for tarpon at least, the coronary oxygen supply to the ventricular myocardium has not necessarily been superseded by air breathing.