D&D 5E The "Perfect" (for me anyway...) Ability Generation System(s)

[ezo]

Here's a fun and easy one that doesn't require excessive rerolls.
3d6, replace a single die with a value of 4.

This yields a range of 6 to 16. If you roll 1,1,1... you replace a die with a 4 and get 6. Similarly, if you roll 6,6,6... replace a die with a 4 and you get 16.

That is a good one, too! I'll have to run the full numbers on it, but quick analysis shows it hits most of the criteria (for myself) without getting crazy.