Thank you for your inputs.
I had heard the rigidity statement, but could never figure out the structural reason why that would happen. So - the truth is now known. Excellent comment of the effects of application of these flutes on a barrel that is already stress relieved. Had not thought of that. Thanks.
SO-- the best way to get a light barrel is too keep it slim. How about these carbon wrapped barrels. Light, stong, and stiff?

? Worth the price on a barrel that just needs repeatable, first shot to first shot accuracy?? (This isn't a barrel for shooting praire dogs -- 338-06) -- OR just go with a slim contour??
Tapper