No. It works like this:
If your taxable income after the standard deduction is $38,000, then the first $9000 of long term capital gains is taxed at zero percent (bringing your income up to $47,000), but anything above that is taxed at 15%. The applicable rate is determined by your total income including the gains. If your total income goes over $518,000, then any additional gains are taxed at 20%. So if you have really significant gains, you still may want to spread them out over time.
