Studying the axons’ membrane permeability at different white matter tracts could clarify the role of aquaporins. Diffusion exchange spectroscopy (DEXSY) is an assumption-free approach to measure water exchange, allowing for any number of exchange processes between any number of compartments. It has never been applied in biological MRI owing to its exceptionally long scan time requirements. Here we present a method to reduce the number of required acquisitions, making DEXSY-MRI clinically feasible for the first time. We apply this method on a nerve tissue phantom, and demonstrate that 14 acquisitions are sufficient to determine the exchange spectrum.