Scrape peeling paint off the ceiling and scrape as much non-peeling paint off as you can. Use a flexible putty/taping knife.
Open up stress cracks in the ceiling by digging them up with the putty knife. Clean out the dust with a paintbrush.
Mix water and trisodium phosphate in a 2-gallon bucket. Wash all exposed areas in the ceiling with this solution. Let the areas dry completely.
Cover the ceiling with oil-based ceiling paint, using a paintbrush. Let the paint dry for 12 hours.
Fill cracks with patching compound, using a brush. Put enough patching compound in the crack that the hollowed-out area will be even with the rest of the ceiling. Apply two coats to deep cracks, but let the compound dry between each application for at least six hours.
Apply a thin layer of joint compound to any indented area in the ceiling. Let the coating dry.
Remove any excess joint compound to ensure that the coat is smooth. Layer on a second thin coat and let it dry.
Sand all compounded areas until they are smooth and the original ceiling is revealed. When you sand the indented areas, just smooth them--don't sand them so much that the original ceiling is seen. Use 400-grit sandpaper. Wipe away dust with a soft broom.
Prime any patched area with a layer of patching compound, using a brush.