Friend Dave had ripped one of the wires on his Sony earbud headphones, MDR-EX38iP, so I decided to fix it. With the help of the Internet he now has a headset back in service.
The wires on these headphones are really very thin and fragile. There is no apparent physical shielding between the signal and ground wires, and twisting like wires together did not get the cut off earbud working. Luckily my friends at Instructables gave me hints to the solution.