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I have a Kreiger Heavy SS Barrel with a 1:11 twist in '06 on one of my Garands. The folks at Krieger claim that because of the nature of the stainless steel they use that it's only safe in a heavy contour. They won't do SS in a G.I. contour for that reason. A .308 or 7.62x51 has similar chamber pressure to an '06 so I'd assume they'd not do a .308 SS with a G.I contour either. Didn't have the heart to ask about a .338 Win mag :D
Now it could be the type of steel Krieger uses, or just their tendency to be over cautious (They also warned about firing the SS barrel in very cold weather - when pressed they said a barrel temp of 0 Fahrenheit or warmer should be fine & couldn't point to any examples of a barrel shattering due to cold alone).
I generally like SS (hence asking Krieger all those damn questions & trying to get them to do a SS with a G.I. contour) & it would be very cool to hear the details on these SS barrels that Mr. Thompson has for sale. (what kind of steel, track record, longevity, etc)