If the broken-off fitting you're dealing with is a brass T fitting, I'd suggest drilling it out close to the diameter of the thread, and using a straight-shank EZ-Out tool to remove the remaining piece. Drive it in until it gets a good bite on the remaining piece of material, and back it out with a Crescent wrench. DON'T use the reverse-helix type of bolt extractor, they just wedge the remains of the fitting tight into the hole.

http://static.zoovy.com/img/usfreight/W100-H100-Bffffff/catsquareeasyout.jpg

I hope that picture link works!
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
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