When I refinish a ring, instead of sanding out dents, scratches and dings, I use a number of burnishing burs to move and push the metal into the dings. (See picture below)
At this point, the surface is fairly smooth. It takes very little sanding to make it flat. I love to use rubber abrasives instead of sanding discs.
If money is tight and you don’t want to spend the $25-35 for the tungsten burnishers you can make one using a used burr. Heat it up to anneal it. I bend it while I am torching it.
For polishing, my number one bench jeweler tip is using a used sanding disc on the mandrel upside-down and charge it with tripoli. You can get into tight places and keep a crisp, flat surface.
This method takes a little bit longer, however, the results are much better then just sanding out blips. Another bonus is that burnishing the ring “work” tempers (hardens) the metal so it scratches less for the customer.
On our custom pieces, after casting, we beat the surface with the burnishers to harden them. Especially the shanks of rings. This works great on sterling silver. Burnishing with the bent burr also can get rid of porosity.