no thanks. No d6 rolling please...
but:
Maybe have fighter attacks that can be used after you rolled a 16+ on your last attack against a foe.
This way you have something like a recharge mechanic that is based on a good attack, that allowed you to position yourself better.
Against a very heavily armored foe, every hit may allow you to take advantage. If you don´t like that, you can define a good hit, if you hit AC+5 (You could even define two AC´s for everyone: normal hit/good hit)
Some great ideas here. It also provides incentives to hit the mooks.....sure I'm not doing as much as if I hit the big man, but it lets me set up my strengths better.
Heck, you could take it a step further and allow manuevers that activate immediately on an attack roll.
Such as:
Disarming Stance: Whenever a fighter in this stance rolls a natural 19 or 20 on his attack roll, he may immediately apply the disarm blah blah.