Background - The management of neonates with complex congenital anomalies depends on careful interpretation of arterial blood gas values. Improved interpretation of these oxygen parameters may allow clinicians to avoid unexpected cardiovascular events. This study examined whether systemic oxygen delivery (Do(2)) can be maximized by the use of indices derived from oxygen saturation measurements in neonates with hypoplastic left heart syndrome. Methods and Results - For the single-ventricle heart with both circulations in parallel, we used a previously developed computer simulation to obtain Do(2) as a function of systemic arterial (Sao(2)) and venous (Svo(2)) oxygen saturation, arteriovenous oxygen difference (Sa-vo(2)), or pulmonary-to-systemic flow ratio (Qp/Qs). We also examined The oxygen excess factor, Sao(2)/Sa-vo(2) (Omega). We found that (1) slight increases in Sao(2) may be associated with large decreases in Do(2). (2) Low values for Svo(2) indicate low values for Do(2). (3) Curves for Sa-vo(2) and Qp/Qs are redundant in the data provided, (Qp/Qs, however, provides these data in more physiologically relevant terms.) (4) High values for Qp/Qs (>4) are associated with low Do(2). (5) Estimating Qp/Qs from oxygen saturation measurements may result in errors when pulmonary venous oxygen saturation is not available. (6) Maximizing Do, is extremely difficult using Sao(2), Svo(2), and Qp/Qs (7) A linear relationship exists between Omega and Do(2), and this linear relationship is not altered by changes in cardiac output. Conclusions - Patients with low Svo(2) values require attention. Ideally, after reducing Qp/Qs to <1.5, Omega might be a better index to guide further therapy and maximize Do(2). Interventions that increased Omega would be considered beneficial, whereas interventions that decreased Omega would be considered detrimental.