1. The intravenous administration of fluid and blood has to balance the danger of unexpected death in response to a reduction of central blood volume (CBV) against that of developing pulmonary and/or peripheral oedema. 2. The initial cardiovascular response to haemorrhage is similar to that developed in response to standing. In the upright position, adults are subjected to a reduction of CBV of approximately 0.5 L and can therefore tolerate a blood loss of approximately 1 L when supine. 3. However, volume administration directed by cardiovascular variables is seldom precise, even with integration of the bradycardia and hypotension developed when CBV decreases by approximately 30%. Immediate intervention is needed because such a reduction in CBV raises the lower limit of cerebral autoregulation to approximately 80 mmHg compared with the commonly considered value of approximately 60 mmHg with an associated risk of developing brain ischaemia and irreversible shock. 4. Alternatively, the volume load can be monitored both directly and accurately by means of thoracic electrical admittance. A functional definition of normovolaemia may be the filling of the heart that ensures cardiac output and oxygen delivery. From that perspective, supine humans are normovolaemic in that a maximal venous oxygen saturation (Svo2) is established. 5. Conversely, Svo2 decreases in the upright position and, with a blood loss of approximately 100 mL, Svo2 is reduced by 1%. It is suggested that, in supine humans and guided by Svo2, normovolaemia may be established to an accuracy of approximately 100 mL and that its adequacy is controlled by recording cerebral oxygenation.