The single-breath method of determining pulmonary blood flow is a simple technique involving no inert gas or special maneuvers such as rebreathing or breath holding. The use of this elegant technique has been limited, however, largely because of questions regarding its accuracy. Previous analyses of the method have indicated that large errors in the estimated blood flow could result if data reduction is not handled carefully. In addition, an uncertain amount of error is introduced, if the CO2 retained by the lung tissue while measurements are being made is not taken into account in the calculations. This paper presents a rigorous approach for estimating the pulmonary blood flow by the single-breath method, which would minimize considerably the effects of measurement errors and would also allow for possible CO2 absorption by the lung tissue. It is based on the exact solution of the underlying equations that describe the dynamics of gas exchange in the lung. The analytic solution provides insight into the difficulties involved in extracting the desired information from the experimental data.