A nipple with a clean break is easier to drill out than a broken screw because the drill will tend to stay centered and not wander into the female threads. I have had good luck with left hand drill bits because with the counterclockwise rotation, sometimes the bit catches and unscrews the broken piece. Always be patient and use a GOOD penetrating oil giving it as much time as you can to work. Recoilrobs' experience with weeks of soaking on a barrel is a good example. I have soaked screws with Kroil and others for days and found totally dry threads a short way down, and credited my sucess to luck. Incidentally, the absolute best penetrating oil I ever used is Cabots' TASGON. It was banned by the EPA in the 1970's because it contains creosote. I have about a pint to last the rest of my life and only use it for extreme emergencies. Watch for it at flea markets and garage sales and guard it with your life. It makes Kroil, PB, Liquid Wrench, and a dozen others I have tried look like weak tea, even on heavily rusted parts. Stinks like the devil when applied daily to rusted exhaust manifold studs, but a week of that has let me break and easily remove nuts on studs that were literally half rusted away in the middle. You can repeatedly heat a pointed copper rod and locally apply heatings to the nipple to get repeated expansion and contraction to help loosen the threads. Vibration from tapping or even an electric engraving pencil may also help the oil find its way down the threads. Last resort on a valuable piece is to find a good EDM machinist as the EDM process will eat away the broken part and not damage the female threads. Good Luck.