Algorithms for estimating cardiac output (CO) from the arterial blood pressure wave have been observed to be inaccurate during changes in vascular tone. Many such algorithms are based on the Windkessel model of the circulation. We investigated the optimal analytical approaches and assumptions that make up each algorithm during changes in vascular tone. Several analytical approaches and assumptions were evaluated on data from 15 critically ill patients by comparison with thermodilution measurements. We found that the most accurate algorithms assumed a constant compliance for the duration of the beat. They produced a percentage error of ±31% by maintaining the compliance and outflow terms in the Windkessel model. For any algorithm, the following assumptions gave highest accuracy: (i) outflow pressure into the microcirculation is zero; (ii) end of systole is identified using the second derivative of pressure. None of the tested algorithms reached the clinically acceptable accuracy of ±30%.