Background: General anesthesia with neuromuscular blockade may facilitate total shoulder arthroplasty but appears to increase risk of cerebral oxygen desaturation. Cerebral desaturation is undesirable and is a proxy for risk of stroke. Purposes/Questions: This study tested the hypothesis that cerebral oxygen desaturation occurs frequently during general anesthesia with neuromuscular blockade and positive-pressure ventilation but does not occur with spontaneous ventilation. Correlations were sought among cerebral oxygen saturation, blood pressure, and cardiac index. Methods: We designed a prospective, observational, cohort study to measure cerebral oxygenation in 25 patients during general anesthesia, both with and without positive-pressure ventilation. Patients undergoing elective shoulder arthroplasty in the sitting position received an arterial catheter, near-infrared spectroscopic measurement of cerebral oxygenation, and non-invasive cardiac output measurement. Moderate hypotension was allowed. Blood pressure was supported as needed with ephedrine or low-dose epinephrine (but avoiding phenylephrine). Hypercapnia (45 to 55 mmHg) was targeted during positive-pressure ventilation. Results: No cerebral oxygen desaturations occurred, regardless of ventilation mode. Under positive-pressure ventilation, the median (interquartile range: Q1, Q3) cerebral oxygenation was 110% of baseline (104, 113), the mean arterial pressure was 62% of baseline (59, 69), and the cardiac index was 82% of baseline (71, 104). Cerebral oxygenation did not correlate with blood pressure or cardiac index but had moderate correlation with end-tidal carbon dioxide. No strokes occurred. Conclusions: There were no signs of inadequate brain perfusion during general anesthesia using paralytic agents. Positive-pressure ventilation with moderate hypotension in the sitting position does not endanger patients, in the context of moderate hypercapnia and hemodynamic support using ephedrine or epinephrine.