The group had stopped for breakfast but, sensing the circling drones, they rushed back to the cars. Moments later, lasers from the Predators lit up the vehicles and the Reaper launched its missiles. Everyone was killed including al-Awlaki and Samir Khan, the editor of an online jihadist magazine. Both were Americans.

The targeted assassination of al-Awlaki, who had been behind a number of high-profile plots, from the Fort Hood shootings to the Christmas “underwear bomber” and an attempt to bring down cargo aircraft with exploding toner cartridges, created a minor stir among civil-liberties groups claiming that his citizenship entitled him to “due process”. But for most Americans it was further evidence that the secret war to protect them from their enemies was going pretty well. Drones had become the weapon of choice. To the surprise of some, a programme that had begun under George W. Bush had been dramatically ramped up by Barack Obama. The former Harvard student and Chicago law professor routinely approved what amounted to execution lists provided by John Brennan, his personal counter-terrorism adviser.

Mr Brennan, a former CIA analyst, is now back at the agency as its director. America’s drone campaign has become symbolic of a new kind of shadow war fought, as Mr Brennan has put it, with a “scalpel” rather than a “hammer”. It is the story of this war, waged in far-off lands by spies, special forces and robotised killing machines, that Mark Mazzetti, a Pulitzer-prizewinning New York Times reporter, tells with some verve and much new detail in “The Way of the Knife”.

In the last month of 2001, after the attack on the twin towers, the White House put the CIA in charge of a global manhunt. While a lumbering Pentagon cranked itself up to deliver “shock and awe” in Iraq, the agency’s counter-terrorist centre became the hub for a campaign to kill or capture anyone connected with al-Qaeda. Mr Bush loved the aggressive hyperbole of its flamboyant head, Cofer Black. By the time the CIA was done with them, Mr Black promised, bin Laden and his supporters would “have flies walking across their eyeballs”. After nearly a quarter of a century when the CIA, humbled by past blunders and scandals, had been legally forbidden to undertake assassinations, the “black ops” boys were back running the show. At the same time, Donald Rumsfeld’s Pentagon, resentful of the CIA’s new primacy in the “war on terror”, was building its own spying organisation. Often the two competed against each other.

Both also turned to private firms, such as Blackwater, that joined the chase for lucrative contracts by hiring former spooks and special-forces types. They provided additional manpower as well as a cloak of deniability for doing stuff that not even the CIA would touch. Mr Mazzetti describes a rogues’ gallery of buccaneering chancers, from Blackwater’s head, Erik Prince, burrowing deep into America’s clandestine establishment, to plausible fantasists such as Michele Ballarin, a Virginia businesswoman who reckoned she could “fix” the failed state of Somalia. There was so much money sloshing around that almost any stunt could get funding (at least for a time) if it had a counter-terror label on it.

But it was the CIA that was and is the big gorilla in the shadow war. Although hurt by the intelligence failures over Saddam Hussein’s non-existent weapons of mass destruction, the CIA’s usefulness to Mr Bush’s White House helped it to recover quickly. Some in the agency worried about the direction of travel, but its political masters were happy to give it cover for most of what it was doing. This included the rendition of terrorist suspects to “black sites”, a network of secret jails in countries outside American legal jurisdiction where prisoners could be tortured and locked up indefinitely without trial. Even when investigative journalists and human-rights groups began to expose some very nasty goings-on in 2005, it was not until Mr Obama became president four years later and signed executive orders banning “enhanced interrogation” techniques, as well as seconding the closure of the CIA’s overseas detention sites, that the agency changed course.

If the capture bit of “capture and kill” was becoming too difficult, the killing was getting easier thanks to both the increasing number of drones that were now available and the expanding network of intelligence sources on the ground to guide them to their human targets. It is a paradox for liberals that the big increase in drone attacks on al-Qaeda camps in North Waziristan (with their inevitable civilian casualties) presided over by Mr Obama was a direct consequence of his attempts to drain the moral and legal swamp left by the previous administration.

The drone campaign still receives uncharacteristic bipartisan support in America and is credited with severely damaging al-Qaeda. But concerns about it are growing, and not just from civil-liberties groups. Mr Obama wants to bring greater transparency and legal rectitude to the way America goes about eliminating its foes, while Mr Brennan appears to want to hand over the operation of lethal drones to the Pentagon. This is partly because it has a clearer military chain of command and partly because there is a growing feeling that the CIA should be doing a bit less killing and a bit more traditional spying. As Mr Mazzetti notes, the obsession with counter-terrorism left the agency woefully flat-footed over the Arab spring and with inadequate assets to support the administration’s strategic rebalancing towards Asia.

Almost the last word in the book goes to one of the architects of the drone campaign, Richard Blee. Now retired from the CIA, he says: “In the early days, for our consciences, we wanted to know who we were killing before anyone pulled the trigger. Now, we’re lighting these people up all over the place…if we are going to hand down death sentences, there ought to be some accountability and some public discussion about the whole thing.” The new American way of war is here, but the debate about it has only just begun. In “The Way of the Knife”, Mr Mazzetti has made a valuable contribution to it.