The big lesson out of all this stuff is: don’t do it again.” That is, don’t invade countries in pursuit of a few Islamic terrorists and turn the whole population against you.

That is the message from David Kilcullen, an Australian academic turned military strategist and one of the most influential advisers to General David Petraeus. Kilcullen, the author of a thoughtful new book on lessons from fighting radical Islamists, is blunt about the operations in Iraq and Afghanistan — and invasions in general.

“Al-Qaeda is already starting to burn itself out”, he says. “Provided we don’t do anything egregiously stupid like keeping invading countries, the trend lines are not good for it.” Iraq, which he calls “a disaster of our own making”, is “exactly the type of conflict we need to avoid”. He agrees that after the 9/11 attacks “there was no option but to do something”. But he holds that the US-led mission conflated “the Taleban with al-Qaeda and the Afghan state with the Taleban”.

Kilcullen’s book, The Accidental Guerrilla, is a perceptive addition to the flood of “what went wrong” books on these wars. It is based on his experience of Iraq, Afghanistan and Indonesia, from within the Australian Army and then on loan to the Pentagon and State Department. It is an argumentative handbook on how to fix a problem.

His argument is that while “there is a global enemy”, it amounts to “only 2 per cent to 5 per cent of the people we’ve been fighting since 9/11”. Many of the others are “accidental terrorists”, provoked into retaliation by intrusion into their territory or disputes. The academic tone shows his roots as a political anthropologist.

His taste is to make more complex the analysis of an already complicated situation. He rejects, for instance, classic theories of counter-terrorism and counter-insurgency in favour of his own, subtler hybrid. He can’t have made himself popular, I suggest, in the brisk simplicity of Donald Rumsfeld’s Pentagon. “No”, he says in one of his more succinct sentences, describing himself as “part of a little insurgency within the US Government”.

But his strength is in knowledge of the different enemies and their motivation, and it is his case that without understanding those subtleties, the battle is lost. His persistence in arguing that the US effort in Iraq was poorly designed paid off. He was helping Petraeus to write his now-famous text on counter-insurgency when the General was put in charge of the failing mission in Iraq, and he became senior adviser to the force. He shrugs off the tag “architect of the surge” of US troops but he did help to make it happen. It was possible, he says drily, “because Secretary Rumsfeld left — was fired — and President Bush directly engaged in what was going on for the first time”.

He is more hopeful about Iraq than Afghanistan, arguing that it “has much more potential for stability”. The “uptick in violence . . . is inevitable as we pull out”, he suggests, but it is not at the moment threatening Iraq’s integrity. The risk, he argues, is that the Obama Administration will pay “too much attention to Afghanistan, and may commit [resources] there to the point whether it cannot respond [to more violence in Iraq].”

But in Afghanistan, while the drugs, violence and control of territory are getting worse, the majority of Afghans are still on our side, he argues. That comes back to his message: know your enemies, and don’t exaggerate or foolishly boost their numbers, or you have only yourself to blame.

The Accidental Guerrilla: Fighting Small Wars in the Midst of a Big One by David Kilcullen, is published by Hurst & Co.

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