2D6 seems a bit extreme (yielding 2-12). Has anyone tried using one or two averaging dice (6 sided dice with faces 2-3-3-4-4-5)? Using 1 averaging dice instead of a d6 would yield APs of 3-11, and 2 averaging dice with yield results from 4-10. Both would have increased chances in the 6-8 range.
The typical variant used by most people is to roll 3D6 and take the highest and lowest value... this makes most rolls in the 6-8 range, but leaves the changes the odds of a 2 or a 12 getting rolled from 1/36 to 1/216, so it happens far more rarely.