On the 2 builds I have with the Bartlein 2b I only had one fluted, its the one in the picture and its a .243. The other one I didn't have fluted - its a 7MM-08. Almost exact same components on each build and they weigh about the same. If I didn't have the .243 fluted it would probably weigh a bit more, if I had to guess the flutes maybe reduced the barrel weight by 3-4 ozs maybe?? Not much I suppose but both rifles balance about the same so I think it did help on the .243. Here is the other one, posted before but likely lost now due to the photobucket fiasco.

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2b in the middle, factory Remington sporter on the left, Brux #3 on the right.

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"Rather hunt Mule deer than anything else"
"Team 7MM-08"