May was a costly month in Iraq: 700 Iraqis and some 80 Americans died, making it one of the bloodiest months of the war. While bombings in Baghdad decreased over the last two weeks as the result of a major sweep by some 40,000 Iraqi soldiers and policemen, backed up by 10,000 troops (Operation Lightning/Operation Thunder), insurgent attacks against Iraqi civilians and police have resumed.

The continuing attacks have generated the usual sort of stories in the U.S. press: America is mired in a Vietnam-style quagmire. Thus a recent Boston Globe report began by claiming: "Military operations in Iraq have not succeeded in weakening the insurgency."

But the Globe is wrong. Coalition operations in Iraq have killed hundreds of insurgents and led to the capture of many hundreds more, including two dozen of Abu Musab al-Zarqawi’s top lieutenants. Intelligence from captured insurgents, as well as from Zarqawi’s computer, has had a cascading effect, permitting the Coalition to maintain pressure on the insurgency.

Vice President Dick Cheney’s recent claim that the insurgency was in its "last throes," however, was clearly an overstatement. But while the outcome in Iraq is far from certain — and even a favorable one won’t come overnight — evidence suggests the United States and the new Iraqi government are on the right track to ultimate success. To understand why, it is necessary to grasp the essentials of the current U.S. strategy in Iraq and how it seems to be playing out.

The Globe’s problem, one shared by most of the American press, is the tendency to see events in Iraq as isolated. They fail to see the overall campaign: a series of coordinated events — movements, battles and supporting operations — designed to achieve strategic or operational objectives within a military theater.

No force, conventional or guerrilla, can continue to fight if it is deprived of sanctuary and logistics support. Accordingly, the central goal of the U.S. strategy in Iraq is to destroy the insurgency by depriving it of its base in the Sunni Triangle and its "ratlines" — the infiltration routes that run from the Syrian border into the heart of Iraq.

One ratline follows the Euphrates River corridor — running from Syria to Husayba on the Syrian border and then through Qaim, Rawa, Haditha, Asad, Hit and Fallujah to Baghdad. The other follows the course of the Tigris — from the north through Mosul-Tel Afar to Tikrit and on to Baghdad. These two "river corridors" constitute the main spatial elements of a campaign to implement U.S. strategy.

This campaign began last November with the takedown of Fallujah.

Wresting Fallujah from the rebels was critically important: Control of the town had given them the infrastructure — human and physical — necessary to maintain a high tempo of attacks against the Iraqi government and coalition forces. In and of itself, the loss of Fallujah didn’t cause the insurgency to collapse, but it did deprive the rebels of an indispensable sanctuary. Absent such a sanctuary, large terrorist networks cannot easily survive, being reduced to small, hunted bands.

With Fallujah captured, the Coalition continued a high tempo of offensive operations. After losing the city, Zarqawi apparently tried to reconstitute the insurgency in Mosul, but was unable to do so because of continued U.S. pressure. In Mosul as in Fallujah, Coalition forces killed and captured insurgents — forcing Zarqawi to move west into Al Anbar province. In March, an Iraqi special operations unit captured an insurgent camp near Lake Tharthar on the border of Anbar and Salaheddin provinces. Such operations forced him back to positions along the Syrian border.

Next came the rivers campaign — to destroy the insurgent infrastructure west and northwest of Fallujah, and so shut down those "ratlines" — which continues apace. May saw four operations within that campaign:

• The first, Operation Matador, was a week-long Marine action centered on Qaim, near the Syrian border. Matador sought to kill and capture followers of Zarqawi known to be located there and to interdict the smuggling routes they used to move downriver to Baghdad. Some 125 insurgents died in the fighting.
• Next came Operation New Market, another Marine operation, in the Haditha area southeast of Qaim. Here, a major highway from Syria crosses the Euphrates and then branches north toward Mosul and southeast toward Fallujah and Baghdad. While the insurgents did not stand and fight as they had in Qaim, the operation still netted substantial intelligence.
• The third was a joint U.S.-Iraqi operation in the Mosul-Tel Afar region that contains the Tigris River ratline.
• The fourth operation of this campaign was the aforementioned Lightning/Thunder in Baghdad itself, which led to the capture of a former general in Saddam’s intelligence service, who (according to the U.S. military) led "the military wings of several terror cells" operating in west Baghdad. Hundreds of other insurgents were captured as well.

The rapid tempo of Coalition operations will likely continue. Indeed, as U.S. and Iraqi forces shut down these ratlines, the insurgency will likely fall back on its "strategic rear" in Syria. Thus, "hot pursuit" into Syria may soon become an issue.

The U.S. strategy in Iraq is limited by a number of factors: the U.S. forces available, Iraqi politics and the time it is taking to create a competent Iraqi military. But the ongoing river campaign indicates that America has chosen to go on the offensive, taking advantage of the success in Fallujah to deny the insurgents respite. The high operational tempo is intended to rapidly degrade the rebels’ lines of communication at both ends of the two river corridors, while killing and capturing as many of the enemy as possible.

But while military operations have weakened the insurgency, military means alone cannot defeat an insurgency. That is why it is necessary to bring the Sunnis into the government. Recent evidence suggests that the steps so far have already begun to drive a wedge between the Sunni and the foreign jihadis who have come to fight for Zarqawi.

Indeed, one of the reasons U.S. forces have been able to go on the offensive — despite the fact that U.S. troop strength is actually lower than it was earlier this year — is an improvement in actionable intelligence. Some of this is coming from captured insurgents. But much of it is coming from Sunnis who realize that their best chance for a future requires them to choose the new Iraqi government and reject the jihadis.

If current trends can be sustained, Zarqawi and his jihadi murderers will soon run out of time and space.

Mackubin T. Owens is an Adjunct Fellow of the Ashbrook Center. He is associate dean of academics and professor of national security affairs at the Naval War College in Newport, R.I. In 1968 he led a Marine infantry platoon in Vietnam.