While the "surge" has not been the overwhelming success claimed by cheerleaders, such as Vice-President Dick Cheney, the policy has at least helped stem the tide of violence, especially in Anbar province where Sunnis are now co-operating in the fighting against al-Qaeda terrorist groups. It has also given US forces on the ground that most useful of military commodities - hope.
Now for the scary stuff:In so doing, Petraeus has also torn up the rule book by rewriting the Army Field Manual that controls US military doctrine. It was a seismic shift: out went big armoured operations and in came a new reliance on the dynamics of asymmetrical warfare. Overnight, or so it seems, US commanders found they had to learn the most important message of counter-insurgency warfare: if the government doesn't win, it loses; if the insurgents don't lose, they win.
Okay, we know that the surge has not done what it was supposed to - give the Iraqis a viable government - but the rest of that paragraph contains information not emphasized much over here.
The other main issue in his bailiwick will be Iran. Already there are some clues. Petraeus has made no secret of the anger he feels about Iranian complicity in the manufacture of the roadside bombs that have killed so many US and coalition soldiers.
Whenever these lethal weapons have been used, he has been quick to blame the Iranian Revolutionary Guards, the organisation that has been fingered by US intelligence as the main culprit for its role in supplying the technology to Shia insurgency groups.
How to deal with it is another matter. Petraeus and Lieutenant-General Ray Odierno, his new man in Iraq, are too cautious to recommend an invasion or even a nuking, but a surgical strike could be on the cards. Just look at what happened in the Syrian desert last September.