Supplementary oxygen is routinely administered to patients, even those with adequate oxygen saturations, in the belief that it increases oxygen delivery. But oxygen delivery depends not just on arterial oxygen content but also on perfusion. It is not widely recognized that hyperoxia causes vasoconstriction, either directly or through hyperoxia-induced hypocapnia. If perfusion decreases more than arterial oxygen content increases during hyperoxia, then regional oxygen delivery decreases. This mechanism, and not (just) that attributed to reactive oxygen species, is likely to contribute to the worse outcomes in patients given high-concentration oxygen in the treatment of myocardial infarction, in postcardiac arrest, in stroke, in neonatal resuscitation and in the critically ill. The mechanism may also contribute to the increased risk of mortality in acute exacerbations of chronic obstructive pulmonary disease, in which worsening respiratory failure plays a predominant role. To avoid these effects, hyperoxia and hypocapnia should be avoided, with oxygen administered only to patients with evidence of hypoxemia and at a dose that relieves hypoxemia without causing hyperoxia.