use sandpaper and polishing papers when finishing my work. I use them for different jobs because they impart different textures on the metal. Sandpaper tends to scratch or abrade the surface and it removes metal fairly quickly. Polishing papers seem to smear or burnish the metal and this burnishing action makes restoring a mirror finish quick and easy.
To restore an already polished surface I start with the finest paper and see if that works, if it doesn't remove the scratch I just move down the order from the finest. This is really the opposite of normal polishing where you start at a coarser grit and move through the finer papers in steps. Because the surface is already polished you can save yourself a lot of time by starting fine and just seeing how coarse you need to go and then reversing your steps back up to the finest paper.