Flow-sensitive alternating inversion recovery (FAIR) is a pulsed arterial spin labeling magnetic resonance imaging method for perfusion quantification. In its standard implementation for quantification with full longitudinal relaxation between acquisitions, its use in time-course investigations of rapidly changing flow values is limited. The time efficiency can be improved by decreasing the repetition time but quantification becomes problematic. This situation is further complicated if a whole-body radiofrequency transmit coil is not used since fresh blood spins will flow in from outside the coil. To alleviate these problems, the use of global pre-saturation is proposed. The resulting expression for the flow signal depends on the relationship between the imaging parameters and the coil inflow time and can be significantly simplified under certain combinations of these parameters. With this implementation of FAIR, quantitative flow maps of gerbil brains were obtained with a 3 minute time resolution in a study of the effects of reperfusion. The pre-occlusion flow measurements were in good agreement with values obtained by the standard FAIR implementation and by other techniques, but the low values following occlusion were underestimated due to the increased transit times.