RE: smallest grain 30-06 ammo?
Factory loaded with .308 diameter bullets about the lightest would be a 125 grain speer hot core loaded by Federal.
Remington still loads the 55 grain accelerator bullet in the 30-06, .308, and 30-30. Midway has them all. The 30-06 product number is 220-009 should you want to try them.
For reloading about the lightest would be 110 grain bullets from Speer, Sierra, Hornady, Berger, and Barnes. It jumps to 125 grain after that.
A warning about the accleerator bullets is that they come out at something like 4100 fps and that translates to a crap load of plastic fouling inside your barrel that is a pain in the arse to get out.
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