Pressing....
The best would be to provide the minimal thickness of compressed face able to withstand the rigours of match play. Hence the theory that the 2 piece face only compresses on the thin strip.
Soft pressing does not equal more power, it reduces the power. If you ask your bat maker to soft press your bat and he says he has either he does not know enough or he is telling a white lie. There is an optimum pressing in each cleft, a peak on a power graph if you need to visualise it, the peak will move around for clefts and so the aim is to assess each cleft before pressing and hit that peak.