When US forces moved in 2004 to oust Al-Qaeda in Iraq from Fallujah, the small city that is the gateway to Anbar province, it took thousands of troops and months of violence. The city of mosques became one of rubble.
"The resources needed to do that were phenomenal," recalls Dr Afzal Ashraf, a former British Royal Air Force group captain who, at the time, was a senior counter-terrorism adviser at the multinational force headquarters in Baghdad.
"The city was leafleted for weeks beforehand to get civilians to leave. And then when we went in with the Iraqis, we went from house to house and room to room trying to clear it."
In total, 13,500 US, Iraqi and British forces in Operation Phantom Fury cleared a core of an estimated 500 Al-Qaeda operatives from the city. The battle left 107 coalition soldiers dead - 95 of them Americans - and 613 wounded.
"I would say it's still the model that can and should be applied," says Dr Ashraf, now a consultant fellow at Rusi, the British defence think-tank.
New targets for the US and its allies include ISIS' economic infrastructure and military positions in civilian areas. US jets blew up a line of 116 oil trucks last week and another 283 in recent days... To reduce the risk of casualties, coalition aircraft dropped leaflets on the trucks 45 minutes before the bombing began, telling the drivers to flee.
A decade later, Fallujah was taken by ISIS, becoming one of the first dominoes to fall in the militant group's takeover of swathes of Iraq and Syria.
The battle for Fallujah is a salutary tale for Western governments as they attempt to step up their military campaign against the terrorist group. US and French presidents Barack Obama and Francois Hollande pledged at the White House last Tuesday to expand air strikes against key ISIS centres, but Mr Obama has largely ruled out any broader shift in strategy.
For many officials and military experts, an exercise in "more of the same" will not be enough seriously to weaken ISIS.
"If we are in a containment phase with ISIS right now, then we are not doing a great job of it," says Ms Harleen Gambhir, counter-terrorism analyst at the Institute for the Study of War. "And a lot of these new proposals are just little things that we can do to try and affect ISIS. They don't add up to a strategy."
Notwithstanding the complex task of securing a political concord over Syria's future - the US and Russia are still at loggerheads over the role of President Bashar al-Assad in a post-war government - there are shortcomings in the parallel military effort and divisions over what any escalation might achieve. The anti-ISIS alliance is also complicated by an increase in tensions between Ankara and Moscow after a Russian fighter jet was downed by the Turkish air force on Tuesday.
Few, if any, policymakers in the West and Middle East seem willing to consider augmenting the aerial effort with the sort of immense ground campaign that many analysts think will be needed - on a scale far larger than the Iraqi "surge" instigated by the US in 2007 for which the earlier battle of Fallujah became the template - if the militants are to be destroyed.
If military planners are serious about destroying ISIS, they need to think about what that will require on land. "Tackling one city at a time is not going to be effective in getting rid of ISIS," he says. "You need to be hitting Ramadi, Tikrit, Mosul and Syria, too, simultaneously. That is a massive operation." At its peak, the "surge" saw about 140,000 US troops deployed in Iraq.
ANTI-ISIS EFFORTS TOO WEAK
For months, some of the most influential military figures within the 65-nation, anti-ISIS coalition have complained that the efforts are far too limited.
In the wake of the Paris attacks, there are some signs that the US-led coalition has become bolder. A senior diplomat in London describes a "new phase" in military operations, characterised by the realisation that caution has carried its own risks too. New targets for the US and its allies include ISIS' economic infrastructure and military positions in civilian areas. US jets blew up a line of 116 oil trucks last week and another 283 in recent days. Such targets had been considered off-limits, in part because the smugglers are not always ISIS militants. To reduce the risk of casualties, coalition aircraft dropped leaflets on the trucks 45 minutes before the bombing began, telling the drivers to flee.
"This was a tidal wave that swept across these oil fields and really crippled them," says Colonel Steve Warren, a spokesman for the US military in Baghdad, of the strikes against ISIS oil operations.
But the bombing campaign is still limited. Mr David Deptula, a retired US air force general, says the US is conducting about six air strikes a day in Syria that actually drop bombs, compared with 1,200 a day during the 1990-91 Gulf war, when he was in charge of targeting. A more effective air campaign could speed up the disintegration of ISIS, he says, saving more civilian lives in the long run.
"We are not giving air power a chance," he says. "We could do it in a matter of weeks, not years." He adds that the excessive caution about potential civilian casualties is "yielding an advantage to our adversaries that I find difficult to understand".
Beyond further use of air power, the option that has been discussed the most by the administration is the establishment of a safe zone in Syria. Supporters say this would provide a haven for refugees and create space for opposition fighters to assemble and receive training. But it has been ruled out by Mr Obama in the past. US defence officials say policing a safe zone would require a major increase in coalition aircraft and a significant commitment of ground forces from a regional ally.
Washington's other options for ramping up the war are even more incremental. They include sending in more special forces to help provide intelligence and call in air strikes; allowing US troops in Iraq to operate nearer the front lines to assist with ground operations; and sending Apache attack helicopters to Iraq to assist local security operations.
But for some analysts, these approaches - even if they were all used - fail to address the central issue.
ISIS is far better armed and prepared - militarily and politically - than Al-Qaeda in Iraq ever was. The struggle that Iraqi Security Forces (ISF) are experiencing in retaking Ramadi gives a hint of the difficulties coalition forces will face.
More than 10,000 ISF troops have been trying to recapture the city for months. It is a test of their ability. Unlike other conflicts with the insurgents, Baghdad has been able to ensure that its operations in Anbar province are free from the participation of Shi'ite militia under Iran's direction that could exacerbate sectarian tensions.
But progress has been excruciatingly slow. Hampered by hundreds of improvised explosive devices, the ISF has barely made it to the city limits.
The problem, says a military official who was based in Baghdad until recently, is that the Iraqis do not have sufficient numbers or mobility. As a result, operations have succeeded in clearing areas - such as the Olympic stadium west of Ramadi in July - only to see them fall back under ISIS control.
"Who will hold the city is a huge question and one that says a lot about how able we are going to be to defeat ISIS," says Ms Gambhir. "ISIS is dug in and the ISF is moving at a snail's pace."
If Ramadi could be retaken, it would only be the start. Iraqi forces would then have a long campaign ahead to secure the Euphrates river valley up through Anbar province.
A strategy to hold territory there would require either the establishment of fortified outposts, in an echo of previous US strategy, or a far larger and more capable helicopter strike capability than the ISF possesses.
In either case, the buy-in of local Sunni militia groups would be essential. Many have little appetite for cooperation with Baghdad or Washington after their alliance against Al-Qaeda - the 2006 Sahwa, or Awakening, movement - was abandoned by its backers and left to be torn apart by revenge assassinations and politicking.
Securing Anbar, according to a coalition diplomat, is Baghdad's first priority, as it relieves pressure on the capital from the insurgents, and because "it's the easiest thing to do".
If pushing ISIS out of its Iraqi cities is hard, the situation in Syria - the focus of so much of the debate since Paris - is even more intractable.
Mr Kenneth Pollack, a Middle East expert at the Brookings Institution, argues that the only way to create a military stalemate that can bring the civil war to an end - other than through an intervention by an outside power - is to create a major Syrian opposition army that can retake territory.
This is essentially a bigger version of the "train and equip" programme that the Pentagon abandoned last month after suffering a series of humiliating setbacks when one group of troops was kidnapped and a second handed over weapons to an Al-Qaeda affiliate. While the principal US role would be to train the opposition army, he argues that a significant deployment of troops would be required to secure a post-war power-sharing arrangement.
"It ( the new army) is going to have to be disciplined, it is going to have to be conventional, it is going to have to be able to hold territory and it is going to need to have a very heavy American presence so that it does not become a new cat's paw of some would-be dictator," says Mr Pollack.
The army would cost US$1 billion to US$2 billion (S$1.4 billion to S$2.8 billion) a year to develop but the US would also need to spend at least US$6 billion a year on air support and another US$1.5 billion to US$3 billion a year on aid, he adds.
The biggest problem in creating such a force could be finding sufficient numbers of effective soldiers. Many in the US defence and intelligence community think a Sunni force battling ISIS would have to be drawn from tribes in the areas it was fighting in. But where militia have fought beyond their traditional areas of interest, they have largely failed to achieve lasting successes.
In eastern Syria, where ISIS' caliphate has its nominal capital, Raqqa, potential recruits for such a force are in short supply. ISIS has killed many men of fighting age there as part of a deliberate strategy, says one US intelligence official. Pre-empting efforts to nurture any form of uprising of Sunni tribes has been a cornerstone of ISIS' strategy, they add.
"Seriously, in terms of beginning to degrade and destroy ISIS, I think we are on a scale of three to five years at the very, very least," says Ms Gambhir.
ISIS, meanwhile, is not sitting still. Its recent attacks in Lebanon, Turkey, Egypt's Sinai region and Paris are part of a coordinated strategy that is as much about securing its territory in Iraq and Syria as about waging global war, says a European intelligence official.
By inciting its enemies into more vicious and precipitous responses in Syria and Iraq, the group's leaders appear to believe it will only make the group stronger by deepening sectarian and tribal divisions in both countries.
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