Senior U.S. commanders say they are optimistic about developments in Fallujah, the troubled Iraqi city west of Baghdad widely regarded as a stronghold for anti-coalition insurgents, including foreign fighters. Yet, none of the coalition's top objectives for restoring order in Fallujah have been met and some western security experts claim conditions there are deteriorating.

General Peter Pace, the deputy chairman of the U.S. military's Joint Chiefs of Staff, the nation's second-highest ranking military official believes events in Fallujah have been positive since U.S. forces pulled out, following a three-week siege in April, and turned over security responsibilities to Iraqis commanded by officers of Saddam Hussein's army.

"There is still work to do, but there is progress being made," he said.

Yet General Pace and other senior military officers acknowledge key coalition objectives in Fallujah have not been met.

These include the removal of all foreign fighters and all heavy weapons in the hands of extremists. The coalition also wants those responsible for an attack in which American contractors were brutally killed and their bodies dismembered brought to justice.

In addition to these unfulfilled objectives, there are reports that Iraq's most-wanted terrorist, Abu Musab al-Zarqawi, may be hiding in Fallujah and is using the city to prepare attacks on targets elsewhere in Iraq.

General Pace says he is aware of the reports, but cannot confirm them even though he and other military officials concede there are armed insurgents in Fallujah.

General Pace believes the coalition did the right thing in pulling out of the city and turning over security responsibilities to an Iraqi force.

"I still believe that the process which we have been following in Fallujah is the correct process," he said. "We certainly have overwhelming military power available to be brought to bear anytime we need to and want to in that city.

"What we have chosen to do, what the commanders on the ground have chosen to do, properly, in my mind, is to work with the city fathers, to work with the new Iraqi interim government to find a peaceful Iraqi solution to an Iraqi problem," continued General PAce.

Pentagon officials note there have been no cease-fire violations in Fallujah since early May, a fact that General Pace calls "a significant success."

U.S. forces carried out an air strike Saturday on a house in the city believed to be a terrorist safe house. Coalition spokesmen say insurgents were killed and ammunition destroyed. But Iraqi military officers dispute the claim and charge civilians were killed.

Coalition officials acknowledge Iraqi security forces do not have full control in the city, and private western security sources paint a startling picture of what is going on inside Fallujah.

These sources, who include former special forces soldiers with close ties to intelligence officials, claim the situation in Fallujah is deteriorating.

According to their information, portions of the city are in the grip of an Islamic Fundamentalism reminiscent of Afghanistan under the Taleban.

The sources report some barber shops in Fallujah have been instructed not to shave men's beards and women risk abuse at the hands of religious police.

The western security sources also report problems with Iraqi police in the city. They say there are allegations truck drivers who sought refuge at a police station were turned over to Islamic extremists for ransom purposes.

It is believed their inability to pay resulted in the murders of at least six drivers whose bodies were recovered recently. The drivers were Shi'ites. Fallujah is predominantly Sunni.

Iraqi police have denied the claims of their complicity in the deaths, calling the charges baseless.

Privately, Pentagon officials say they are concerned. Yet they continue to indicate that despite the coalition's acknowledged military capability to go in and clean out Fallujah, they have no intention of doing so, for fear of incurring heavy casualties in bloody door-to-door fighting and to avoid turning the city into a rallying point for insurgent forces.

Instead, these officials suggest what the U.S. led coalition is doing is watching and waiting, in particular, watching and waiting to see what the Iraqi security forces in Fallujah do. They see it as a learning process for both the coalition and the Iraqis, and indicate some course corrections are likely.

These officials, speaking on condition of anonymity, say there is no timetable to achieve their security objectives in Fallujah. Yet without offering any explanation, they predict that a year from now, the situation will be much better.

Correspondent Alisha Ryu in Baghdad contributed to this report.