We present a study of the annealing of non-equilibrium structures on Ni(001). The non-equilibrium structures are produced by sputtering, and are investigated by scanning tunnelling microscopy. We find that, depending on the precise amount of removed material, the surface morphology evolves towards equilibrium along different pathways. This reflects itself in differences in the large-scale patterns that form and the time and temperature dependences of the restoration processes. We explain these differences in terms of the atomic-scale diffusion mechanisms responsible for the surface mass transport. Two of these pathways, ripening and coalescence of vacancy islands, are studied in more detail. We observe local correlations in Ostwald ripening and find anomalous behaviour of vacancy islands when these are in close proximity to each other.