As far as I can find Steven, there are really only ascetic advantages to a fluted shaft. My Odyssey putter has about a 4 inch fluted section in the shaft about 8 inches or so above the head. I know in gun barrels, fluting is done to reduce weight, and to remove heat on a bull-barrel, used in some aluminum archery arrows to reduce air drag, and improve flight stability, but neither of these should apply to a putter - (unless you're chunking it after a missed putt

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I wouldn't think that weight would be the reason, but in a full-fluted shaft, I would think it would increase the stiffness of the shaft??