I used to fly A330/340/346 for LH and the 330 /346 have a derated climb thrust option. At my company that is because they bought thrust instead of engines, and as the engines are continously monitored anyways, the thrust is what the company pays for. So if you are lighter, you use derated climb thrust, simply by typing D1 or D2 into the FMS Performance page. If you need full climb thrust, you clear it. SOPs called for D1/D2 at certain T/O weights.
And having someone call my beautiful A343 engines, that never failed me in endless hours, "hairdriers" hurts, hurts very much, but the man is right. Even though they got me above the 747s on the crossing every time...
edit: the Cost Index does not have an impact on the thrust output at all, only on the climb/cruise/descent speed and optimum level on the progress page, just like on an A319...