The most significant hurdle to the development of a safe and effective hemoglobin-based oxygen carrier ("blood substitute") is generally thought to be its propensity to cause vasoconstriction in the microcirculation and hypertension. Two theories for this effect are currently being studied: in one, scavenging NO by hemoglobin reduces vasorelaxation; in the other, cell-free hemoglobin oversupplies O2 (a known vasoconstrictor) to vascular walls by facilitated diffusion. While both mechanisms might lead to reduction of local NO concentration, the important distinction between the two is that if the NO scavenging theory is correct, it greatly diminishes the prospects to develop any solution based on free hemoglobin. However, if the O2-oversupply theory is correct, modifications to the hemoglobin molecule can be envisioned that can prevent oversupply and reduce toxicity. This review summarizes the development of Hemospan, a novel modification of human hemoglobin whose design is based on the O2-oversupply theory. Because of its low P50 and increased molecular size, the release of O2 in resistance vessels (arterioles) by Hemospan is restricted, and vasoconstriction is greatly reduced.