Classical pharmacokinetic models used in computer-controlled infusion pumps (CCIPs) assume instantaneous mixing of drug in blood; however, the average recirculation time of blood in man is approximately one minute. To investigate the effects of recirculation dynamics on the transient performance of CCIPs, we propose a hybrid physiologically-based pharmacokinetic model for the narcotic alfentanil. A three-compartment model was derived from the response of the hybrid model to a short infusion and used to compute a CCIP infusion targeting 450 micrograms/l. For this infusion, the hybrid model predicts that the arterial plasma concentration will overshoot the target concentration by 39 percent with an average prediction error of 3 percent. The overshoot and average prediction error increase to 100 and 25 percent respectively when using a three-compartment pharmacokinetic model derived from a bolus. The overshoot can be reduced by decreasing the maximum possible infusion rate, or by increasing the zero-order hold infusion interval.