It's been a while since I was involved with it, but I recall that the criteria for cut-back on departure etc was based on minimising the noise exposure contours based on noise/power/distance tables for the aircraft/engine combination and associated climb performance.
The
Integrated Noise Model is a software tool for predicting community noise exposure.
There are over-riding constraints such as minimum engine-out climb gradients etc, but there will usually be an optimum point where the noise reduction for power reduction outweighs the increase in the contour due to the reduced climb rate.