Thanks for those contributions, I have looked at the references you suggest Mutt. The community noise document is pretty vague, in summary it says noise is a difficult subject to quantify and one should refer to individual operators for more information.
The combination of derate, assumed and improved climb is what our EFB churns out pretty much by default. Previously with paper tables I found it easier to get an overview of what we were doing. Now a small change in a non limiting situation can result in a different flap setting and derate without it being obvious why. The EFB tries to get the lowest takeoff thrust setting for the weight and conditions. The result is what another contributor wittily referred to on another thread as high idle takeoffs. I have seen no evidence that noise is taken into account.
In one of the training courses there is a graph showing the effect of improved climb. It shows clearly from the start of the takeoff run that the point where the improved climb crosses above the unimproved is half way to 3000 feet. Thus my hypothesis that if we speed up at 1500 feet or below there does not seem to be much climb performance benefit and there is a significant increase in noise for the airport's neighbors.
If I have understood Haughtney correctly then the increase in thrust seems to occur on most 777 takeoffs as well, although unless you live at the end of the runway in Dubai you will probably be less concerned by this then by the sheer volume of takeoffs by 737s at most other places.
What has got me thinking is the significant increase in complaints from people living around airports in Germany at a time when traffic has not really increased. The new runway in Frankfurt has led to changes in where planes fly and therefore annoyed people who were previously unaffected. But I wonder if some of the recent operational changes like those mentioned by myself and Denti who flies for the second largest airline here are also contributing.