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.