Exchange of nuclear magnetization between spin pools, either by chemical exchange or by cross-relaxation or both, has a significant influence on the signal attenuation in stimulated-echo-type pulsed field gradient experiments. Hence, in such cases the obtained molecular self-diffusion coefficients can carry a large systematic error. We propose a modified stimulated echo pulse sequence that contains T2-filters during the z-magnetization store period. We demonstrate, using a common theoretical description for chemical exchange and cross-relaxation, that these filters suppress the effects of exchange on the diffusional decay in that frequent case where one of the participating spin pools is immobile and exhibits a short T2. We demonstrate the performance of this experiment in an agarose/water gel. We posit that this new experiment has advantages over other approaches hitherto used, such as that consisting of measuring separately the magnetization exchange rate, if suitable by Goldman–Shen type experiments, and then correcting for exchange effects within the framework of a two-site exchange model. We also propose experiments based on selective decoupling and applicable in systems with no large T2 difference between the different spin pools.