Jumping back to John Tullamarine's post, I heartily agree with his caution regarding 'too rapid' thrust advance following engine failure during a Flex / Assumed Temp. Thrust takeoff. Having coped with the initial yaw following engine failure, it is common to see trainees in the simulator unprepared for the additional rudder input required for the additional thrust.
Flight testing / certification procedures still use the 'Full Thrust Rating' thrust when considering Vmca / Vmcg, and adequate control should exist, within the certification parameters, to advance to the full thrust rating. It is considered normal (although technically not required) by most operators to do so.
Where great caution is required is when the aircraft is certified with several different thrust RATINGS for the same engine, e.g. the RR Trent has a 100%, 92%, and 80% rating, selectable for the particular operational requirement for a given takeoff. Vmca / Vmcg DOES consider the lower rated thrust, and if REDUCED thrust is used against a DERATED thrust, pilots should be VERY cautious in only setting the RATED thrust following engine failure. For the RR Trent example, engine failure during takeoff using the 80% rating could lead to dire consequences if thrust was advanced to the full 100% rating (it's possible) at V1/Vr/V2 speeds.
The same caution applies to engines which operate normally on full Takeoff thrust rating, but employ 'overboost' (e.g. Automatic Performance Reserve (APR)) as an option. In these cases a takeoff with APR off and appropriately set V1/Vr/V2 could lead to control problems if thrust was manually advanced to APR following engine failure.
Read carefully, don't confuse Derated thrust with Reduced thrust in these lines.
(The 100%/92%/80% RR Trent ratings I refer to here are for my current aircraft. It is accepted that other operators may use different derates, as a customer order from the manufacturer).