When I read the posts above, I am confused. Both B 777 and B 737 NG are fitted with ECC, yet you get full rated thrust for B 777 and derated thrust for B 737 NG when you firewall the thrust levers (according to some posts above)?
No, they behave the same. Firewalling gives you full rated thrust on the 737 NG (the classic can give more than full rated thrust overboosting the engine in the process), which is a very unwise thing to do when using a derate.
@Intruder, the 737 NG is certified for using a combination of derate and assumed temperature as factory standard, the 737 classic need an AFM supplement but can be certified for the same as well. We use it on our 737s every single take off. Yes, it can be quite weird to take off with a N1 of 76% (derate 2 18k and over 60° assumed on the -700), but you get figures like that only on 4km runways with a low obstacle situation.
As barit says, using more than calculated thrust in the one engine out case is something not to do unless you checked the full rated VMCg/a and are above those speeds. Something you usually do not have the time to do during a V1 cut. Therefore our SOP is to just leave the thrust where it is until clean up is completed as the performance is calculated for the OEI case anyway.