In the pulsed arterial spin labeling (ASL) techniques EPISTAR, PICORE, and FAIR, subtraction of two images in which inflowing blood is first tagged and then not tagged yields a qualitative map of perfusion. An important reason this map is not quantitative is that there is a spatially varying delay in the transit of blood from the tagging region to the imaging slice that cannot be measured from a single subtraction. We introduce here two modifications of pulsed ASL (QUIPSS and QUIPSS II) that avoid this problem by applying additional saturation pulses to control the time duration of the tagged bolus, rendering the technique relatively insensitive to transit delays and improving the quantitation of perfusion.