This may be old news, but it was news to me.  Hope it saves you lots of grief.

I had stripped the Phillips head on a screw in my gear shift mechanism.  And yes, it happened because I was impatient and didn't wait until I could find the impact driver.  How many times do I have to learn this lesson?

Anyway, there was no way to cut a slot in the screw head, and the existing Phillips slots were too buggered for the now-found impact driver to work.  I was about to drill out the screw and then at least have to clean out the threads with a tap.  More likely that I would mess up the threads in the block and have to redrill and retap the hole.

In an inspired moment (thanks, Tecate), rather than drill out the entire screw, I drilled a hole about 1/2 the diameter of the screw (the screw, not the head of the screw) and about 1/3 the length of the screw.  I hoped that this hole would give the point of a Phillips impact bit somewhere to go rather than just bottoming out before its sharp edges could engage with the screw head.
 
A couple of whacks on the driver and it came out beautifully, in one piece.  In the picture you can see the 4 marks from the impact bit.

Pointers:  1) Don't make the hole any bigger than 1/2 the screw's diameter.  This way you leave plenty of metal and you're less likely to just twist the head off.  2)  Use a relatively pointy bit, to insure that the point can go down the hole a ways, enough to let the edges of the bit engage.

Or even try a Left Hand drill bit and revering drill motor. Or the neat drywall screw extractors I found at Sears. Have worked every time for me. A variety of styles both internal grabbing and eternal screw head grabbing. YEMV. Max

runrun wrote on 08/04/11 at 07:31:08:


Another thing to try with your 18v drill, is to loosen the clutch and and let it vibrate the screw while putting a lot of torque on it.

Another trick I used one time was to simultaneously vibrate the screw head with an engraver, while torquing the screw.  I flattened one of the engraver bit so it would buzz the head of the screw. It took two guys, and some heat, and some ATF used as penetrating oil, and a little time, but after a couple of minutes, the screw backed out without munging up the head.

One other trick:  heat and cold at the same time.  
 -- Heat the whole area as much as you can without damaging anything, then have one guy torquing the screw as hard as he can while the other sprays the head of the screw with one of those compressed gaseous dust removers.  
 -- The stuff coming out of those dusters is very very cold, and for a few seconds you'll have the screw contracting from the heated-up surrounding metal.  
 -- We do this in avionics sometimes where things like impact drivers are way too brutal.

runrun wrote on 08/04/11 at 04:43:59:

114 times... ...

If you can stop with the screwdriver when it starts to cam out of the slots, you can use a pin punch & drive the meat back where it came from, BUt. If you spin the driver & sling the metal off the head of the screw, well,, yer screwed.