Engineer:
My apologies; I thought you were asking a type-specific question and not a general one. Without getting myself into a nit-picking discussion about the finer points of Performance "A", perhaps I could give you a rather basic explanation of "derate" or "reduced thrust" take-offs?
It is often the case that an aircraft is not being operated to its absolute limit. For example, if the runway is much longer than that actually required or the load means that the aircraft is below its optimum weight for a given runway then a derate take-off is possible and allowed.
There are of course many other considerations such as obstacles and terrain considerations after take-off to be considered. We pilots consult performance tables called RTOGs (Regulated Take Off Graphs) and they will tell us for any given set of conditions exactly how much we can safely derate by.
From the noise point of view this is obviously desirable. A 10% reduction in take-off power would probably result in more than a 10% reduction in noise (but I'm only guessing).
On the debit side, the take-off run will obviously be longer and the aircraft will not climb quite so quickly. However, it is doing all of this whilst making a hell of a lot less noise! When it comes to the positioning of that particular airport's noise attenuators, it might not be quite so easy to make a choice.
For example, is it better to upset the people in the car park of Birchanger Services on the M11 or the entire populace of Bishops Stortford?
The other huge advantage of doing derate take-offs is that they are so much kinder on your engines. We should always be kind to them for you never know when you are really going to need them. Quite clearly, if you derated on every take-off versus going at full power on every take-off, it would not take rocket science to work out which engine is going to last the longest.
In fact, some engine manufacturers give credit for derate take-offs. When I flew DC-10s every single derate was faithfully entered in the tech log (even if it was just 1%) and due credit was given by GE.
I hope this is of use.