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The structural dependence of the magnetocrystalline anisotropy of itinerant permanent magnets (or nanostructures of iron-series 3d elements) is investigated by model and tight-binding calculations. Magnetic nanostructures yield strong oscillations of the anisotropy as a function of the number of d electrons per atom, which can be tuned by alloying. While interatomic hopping is usually more important in metals than crystal-field interactions, we find substantial crystal-field corrections for some configurations, especially for the atomic square. Finally, we compare our results with Néel model.