For the first six months of the troop escalation, high rates of violence continued unabated. That is suspicious. What exactly were US troops doing differently last September than they were doing in May, such that there was such a big change? The answer to that question is simply not clear. Note that the troop escalation only brought US force strength up to what it had been in late 2005. In a country of 27 million, 30,000 extra US troops are highly unlikely to have had a really major impact, when they had not before.
As best I can piece it together, what actually seems to have happened was that the escalation troops began by disarming the Sunni Arabs in Baghdad.
Once these Sunnis were left helpless, the Shiite militias came in at night and ethnically cleansed them. Shaab district near Adhamiya had been a mixed neighborhood. It ended up with almost no Sunnis. Baghdad in the course of 2007 went from 65% Shiite to at least 75% Shiite and maybe more. My thesis would be that the US inadvertently allowed the chasing of hundreds of thousands of Sunni Arabs out of Baghdad (and many of them had to go all the way to Syria for refuge).
Rates of violence declined once the ethnic cleansing was far advanced, just because there were fewer mixed neighborhoods. Michael Ware:
http://thinkprogress.org/wonkroom/2008/04/03/ware-sectarian-cleansing/' The sectarian cleansing of Baghdad has been — albeit tragic — one of the key elements to the drop in sectarian violence in the capital.... It’s a very simple concept: Baghdad has been divided; segregated into Sunni and Shia enclaves. The days of mixed neighborhoods are gone....
If anyone is telling you that the cleansing of Baghdad has not contributed to the fall in violence, then they either simply do not understand Baghdad or they are lying to you.' http://www.juancole.com/2008/07/social-history-of-surge.html