Variant Rule: Automatic Miss Confirmation

It's always bugged me that all characters have at least a 5% chance to miss on any given attack roll. Worse, the more skilled a character is, the more attacks he has per round; the more attacks he has per round, the greater the chance he'll mess at least one of them up.

The DMG proposes a variant rule that gives an attacker a bonus of +10 on a natural 20, and a penalty of -10 on a natural 1. This bugs me, too, having such a steady distribution between 2 and 19, and then blowing up on a 1 or 20.

Actually, I'm cool with the automatic hit on a 20, but wouldn't mind a better solution to the automatic miss problem than the DMG's variant rule. This got me thinking, and I've come up with what may be the foundation for a decent rule. I'm sure it will need some tweaking, but here's my initial thought:

VARIANT: AUTOMATIC MISSES

     When you make an attack roll and get a natural 1, immediately make another attack roll with the same modifier, but also apply a -10 penalty. On this second attack roll, treat a natural 1 as an automatic failure. If the second attack roll is successful, treat your original roll as a 1, and apply any attack roll modifiers. If the second roll is a failure, you have missed your opponent.
     Example: Bob's character, Tordek, has an attack bonus of +16. He tries to attack an orc with an armor class of 13. Bob rolls his d20, and gets a natural 1, so he makes a second roll. On this second roll, Bob gets a 9, which is a success (9+16-10=15 vs. AC 13), so his original attack roll stands as a 1. Applying his modifiers, his final attack roll result is 17 (1+16=17 vs. AC 13), so Tordek hits the orc.
     If Bob had rolled, say, a 6 on his second attack roll, the result would have been a failure (6+16-10=12 vs. AC 13), and Tordek would have missed the orc.

I think the penalty to the second attack roll may need to be tweaked, and, further, may need to be variable rather than fixed. Any thoughts?