A D&D die rolling method that produces good results with variety

I've decided for the sake of D&D players everywhere to make a permanent recording of my stat rolling method.   Here it is in order.

1.  For each of the six stats in order roll 3d6.
2.  If the sum of all stats is greater than or equal to eighty then you are done.   Go to step 4.
3.  Reroll the lowest stat using 3d6.   Go back to step 2 and proceed from there.
4.  Exchange any two stats.

Example #1 -- I'll play a fighter.
rolls 10, 10, 7, 13, 14, 8

Step #1
Strength 10
Intelligence 10
Wisdom 7
Dexterity 13
Constitution 14
Charisma 8

Total is 62  we are short of 80 by 18!

Step #2 reroll wisdom 17!
Strength 10
Intelligence 10
Wisdom 17
Dexterity 13
Constitution 14
Charisma 8

Total is 72 and we are still short of 80 by 8!

Step #3  reroll charisma  11
Strength 10
Intelligence 10
Wisdom 17
Dexterity 13
Constitution 14
Charisma 11

Total is 75 and we are still short of 80 by 5.

Step #4 reroll strength (player chooses if there is a tie)  12
Strength 12
Intelligence 10
Wisdom 17
Dexterity 13
Constitution 14
Charisma 11

Total is 77 and we are still short of 80 by 3.

Step #5 Now we must reroll Intelligence.  14
Strength 12
Intelligence 14
Wisdom 17
Dexterity 13
Constitution 14
Charisma 11

Total is 81 so we can stop.

Step #6 exchange any two stats  (Strength and Wisdom)
Strength 17
Intelligence 14
Wisdom 12
Dexterity 13
Constitution 14
Charisma 11

Notice that we have a pretty decent fighter character.  Notice also that we have a smart fighter which is not something you normally get from point buy systems.