I do things the long way, and use 600-800-1000-1500-2000-3000 trizac before using a polish. All these are wet-or-dry and available at the body shop supply store, some at autoparts stores too. Always with water, and a light reflecting on the surface. Each stage rotates the sanding direction 90 deg and sand until all the previous lines are gone. The parts come out crystal clear and glossy. Works great on watch crystals (non glass) too. Tried on the wing tip lenses that are soft and took out a bad scratch. Be selective on what grit to use initially based on the scratch to be removed. Always use a foam backer to avoid finger pressure lines.
The papers can be used many times and don't degrade very fast. Trizac is the most expensive. They also make a Trizac 5000, but have not found the need.
Not as manly as power tools, but the results are like new.