Long term capital gains

Are long term capital gain tax rates similar to the ordinary income tax brackets whereby the first $44,625 of gains (including any other taxable income) is taxed at 0% and anything beyond that is 15% (until the next limit) or is it more like a cliff that if you go over by even a dollar you are bumped up to the next bracket for the full amount of your capital gains? I have very little ordinary income/dividends/interest, so I want to sell stock up to the amount that I pay no capital gains and am wondering how careful/conservative I need to be, to not go over the 0% threshold.