There are two that I can think of off of the top of my head.
1) roll stats and then allow the player to switch a pair of them so that a high stat can be placed into the prime for the character concept. Random and control.
2) roll stats and allow stats to be lowered by 2 points in order to raise another stat by 1. Random and control.
I used both somewhere around 25 years ago, although in my case, the point swap was limited points from one stat to points to one other stat, but could be made at a 1:1 trade. This was an attempt to deal with the fact that most characters in 1e AD&D needed at least one 16, and were often incredibly stronger if they had even a single 18. Thus, you could usually make a character of some sort with one 18 if you wanted it. I did away with that method when it became clear in the context of 1e, most people where just dumping points from charisma into their highest stat.
But again, the swapping method only addresses one issue with randomness. It doesn't deal with the bigger issue of having a level playing field.
The methodology I'd lean toward now if I was forced to allow random ability score generation in D&D and depend on it is this:
a) Pick an ability score. Roll 3d6 straight up N times and take the result you want.
b) Repeat 'a' for a the remaining ability scores, in the order of your choosing. But each time you've taken a 16 or higher in a prior step roll 3d6 1 less time in all subsequent steps (minimum at least once). Alternately, taking 18's might deduct 2 dice; I'd have to play test this.
c) Everyone must watch you roll, and you must keep what you get and play it in good faith. This should not be hard, as for N = 6, you'll have pretty darn good stats. By controlling N, the group could set the average power level where they wanted it. And because the stats are guaranteed to be good and have very few terrible results.
That might work pretty decent, pending testing, but its horrendously complicated to perform this method with multiple players using real dice. And the temptation to cheat and all the consequences of that is still there, as I'm sure there would be that one guy that took 16+'s in everything and then said, "Alright. I got an 18 off of 3d6 straight up." Because, people.
