Instead of Vanilla 2d6

My work back here rolling "lower of two dice" made me wonder if I could emulate a 2d6 curve that way. " 7 + (lower of 2d8) -- (lower of 2d8) " turns out to be almost indistinguishable from a 2d6 curve! Were I actually using this die mechanic for something, I'd be tempted to have results of 0 and 14 "explode" with further "lower of 2d8" rolls.

Tabletop play seems to have a tension between providing interesting results (usually means increasing numbers of dice) vs. keeping record keeping reasonable (means keeping pip totals small). World of Darkness and Shadowrun solve this by rolling lots of dice and counting each die as a pip; Betrayal at House on the Hill is similar, in that its dice are numbered from 0 to 2. ...I guess my personal holy grail here would be a simple, manual die mechanic that'll produce a smooth 1/x curve.

2d6 is really easy to use on the tabletop. It does have some problems--cannot roll higher than 12 or lower than 2, "lucky" streaks are pretty common, and "unlikely" results may be more or less common than players think appropriate.

My first thought is that I can break "lucky" streaks by rolling lots of times and discounting all results until a given value has been discounted a certain number of times. (The quota for each value would be proportionate to the chance of rolling that value.) This would be terrible to execute manually but could work with a computerized die roller.

My second  thought is to replace 2d6 with 4d6 / 2. This makes middling results more likely and extreme results much less likely.

I'm not sure I'd want to use any of these as a straight replacement for 2d6 rolls in (say) BattleTech, but I think it might be interesting to designate individual pilots as cautious (4d6/2) or swingy (quotas).
(I'd like to eventually do my own computerization of BattleTech, and I have some thoughts on how I'd modify specific BattleTech mechanics, but that's not a project I can start soon.)