It is a long time since I did a derated thrust take off or even the calculation.
I believe that Air new Zealand was the first to use this system on the DC8-52.
The criteria was that a derate(Wannabe term Flexithrust)was allowed only if there was a runway margine available.
i.e 8000 ft of runway needed for the given weight/ambient/wet,dry, wind performance, but there was 11000 ft of concrete available.
So we could derate to use not more than 80% (8800ft of available runway.
One could not do a balanced field operation ( to cross the far threshhold at 35feet with a critical eng failure AT V1 and maintaining V2)
Having said that, if one was on a derate take off and did loose one after v1; one had to have precalculated the VMCG and VMCA so that normal take off thrust could be applied to the remaining power plants if the vmc/a/g crit was superceeded.
It was also similar in the Bae 11-500, not counting noise abatment climbs.
They could be bloody spookey at places like Luton.