If I may....
I think what "barit1" is trying to say is...
The Vmcg value is different between derated and assumed temp reduced thrust takeoffs.
Basically, when derated thrust is used, the takeoff Vmcg is still calculated using maximum thrust, since the derated thrust setting may be increased during the takeoff, if considered necessary.
But when assumed temperature reduced thrust is used, that is the thrust setting used to calculate Vmcg, since (except in real emergencies) that is considered the maximum thrust setting for the takeoff.
So, as you can see, in some shorter runway situations, you can sometimes lift more weight with a/temp reduced thrust than you can with derated power, simply because of the restriction on V1 with regard to Vmcg.
Am I making any sense here?
Cheers...FD