Morphological changes related to neurological diseases occur at micrometer scales. Obtaining such information non-invasively opens new paradigms for clinical diagnosis. We use the Non-uniform Oscillating Gradient Spin-Echo sequence to estimate microstructure size-distributions with high sensitivity based on probing a signal “decay-shift” rather than a signal decay-rate. The “decay-shift” arises with sharp gradient modulations. As fast ramps are prohibitive in clinical diagnosis, we evaluate the method using sharp and smooth gradient modulations. We show using simulations and proof-of-principle experiments with phantoms that mimic axon-bundles, that optimal estimation of the underlying microstructure-size distribution is obtained either using sharp or smooth modulations.