I saw a good demonstration of how these parallel tax brackets work when I was preparing my own taxes back in 2008, the year I cashed out my company stock and ERed. (I was able to cash it out using NUA, or Net Unrealized Appreciation, and as a result most of it was taxed as LTCGs just like QDs are.)
My taxable income, excluding the huge LTCGs, was in the 15% bracket. This meant that a small portion of the LTCGs from the sale of the company stock ended up being taxed at 0% with the remainder of it (most of it) taxed at 15%, the highest rate applicable at the time. Of course, while this huge LTCG was mostly taxed at only 15%. it still tossed the rest of my income into the AMT so the small saving from having some of that income taxed at 0% was dwarfed by how much more I had to pay from the AMT. Still, paying only 15% on that huge, lump-sum payout was a key part for me to be able to ER when I did.
Retired in late 2008 at age 45. Cashed in company stock, bought a lot of shares in a big bond fund and am living nicely off its dividends. IRA, SS, and a pension await me at age 60 and later. No kids, no debts.
"I want my money working for me instead of me working for my money!"