So you twisted the head off a brass wood screw — bummer. If you try to back out the remaining screw with a reverse-thread screw extractor, you may just deform the soft brass rather than remove it. And if you grab the broken screw with pliers, you could end up doing more damage. It might be time to try these broken screw extractors from WoodCraft.
Chuck the screw extractors into your drill to bore a clean hole around the screw threads, and pull out the remaining plug, broken screw and all. You can easily patch the remaining hole with a bung, leaving little evidence of your error.
The 2″ long hollow extractors have saw toothed edges on both ends for twice the life. With the 3/8″ extractor you can remove up to #12 screws, while the 5/16″ and the 1/4″ extractors leave smaller holes when removing smaller screws. They run about $10 to $12.