So... 3d6 six times, assign in the order they're rolled, and assign 14 to one stat. I've further thought about this and I've rolled a bunch of pregens (with purple sorcerer's DCC 0-level character generator, you can get 4 at a time) to test this system see how it goes. I'd say that about 75% of the characters rolled up were playable, i.e. not too shaby and not disturbingly powerful either.
So I've come up with two additional options to even out the playing ground. The method (until someone comes up with a better idea anyway

) is as follows:
1) you are born: choose race (yes, race before rolling things up!). Do not apply racial ability score bonuses yet.
2) natural selection: roll two sets of stats, each 3d6 assigned in the order they are rolled. Pick the one you wish to keep.
3) character development: if you wish, set one ability score value to 14 instead of the value that was rolled up
4) nobody's perfect: if you do not have at least (a) one ability score of 7 or lower; or (b) two ability scores of 9 or lower: assign a value of 7 or lower to one ability score of your choice. If you do not, restart the process from scratch.
5) apply racial bonuses to your stats.
I wish to avoid the really crappy PC: offering the choice between two sets of ability scores and assigning 14 to one stat will probably avoid this in most circumstances.
I also wish to avoid the super heroic PC, thus the restriction in #4. I want the PC to have at least one weakness even after racial modifiers are accounted for.