The hard-edged aggressiveness of combat operations of just a few months ago is being replaced with a seemingly softer, hearts-and-minds practice.

Soldiers who sometimes kicked in doors and gates to homes in tense neighborhoods in the push to root out extremist gunmen and their supporters now knock and request permission to enter, then engage in less confrontational conversation while a search takes place for illegal weaponry.

Civilians, especially children, shooed away during patrols of neighborhoods are now encouraged to stop and chat.

Soldiers are increasingly becoming ombudsmen, social workers, aid brokers and reconstruction project managers in the effort to make Baghdad's neighborhoods inhospitable areas for gunmen who may attempt to re-infiltrate the capital or reassert influence.

Overall, attacks of all kinds in the Baghdad area in July fell for the third consecutive month. In July, for example, there were 95 incidents. In April there were 740 compared to 1,150 in July 2007, according to the U.S. Army's 4th Infantry Division.

The number of vehicle-borne explosive attacks last month was just one, resulting in six casualties, as opposed to 42 attacks and 186 victims in July last year.

Nonetheless, Iranian-influenced "special groups" -- offshoots of anti-American cleric Moqtada Sadr's Mahdi army -- remain a "long-term threat to the security of Iraq and its people." The insurgent gunmen are keeping a lower profile at present but are "still not adhering" to the ceasefire reached May 12 between Sadr and the government of Iraqi Prime Minister Nouri al-Maliki, officials said.

Al-Qaida in Iraq, although seriously degraded, can't be written off either.

"[Al-Qaida] attack levels show they don't have the capability they once had," Col. Allen Batschelet, chief of staff of the 4th Infantry Division said recently.

"Are we concerned about them coming back? We are always concerned about terrorist active or individuals who want to do bad things in Baghdad," Batschelet said. Then added: "We've been very aggressive in and around the city."

Staff Sgt. Robert Rollheiser and the men of Echo Company, 1st (combined arms) Battalion, 68th Armor Regiment, are typical of the transformation taking place in Baghdad. In April and May, the company of combat engineers sought out and destroyed scores of improvised explosive devices (IEDs) in southern Sadr City while fending off snipers as part of operations to erect a security barrier wall in the area. Today, with Iraqi forces performing most IED operations, they're visiting neighborhoods, knocking on doors and combing markets looking for extremist holdouts.

"We're going back to the market in muhalla [neighborhood] 343 to stir things up a bit," Rollheiser said during a pre-mission brief at COP (combat operations post) Callahan, located in Baghdad's Shaab district. "We know the leaders of JAM ['Jaysh al-Mahdi' or Mahdi Army] and the special groups have run but there are others left who are coming into our district. We can't catch them all. We can't kill them all. But we can make their lives [expletive] difficult."

Shaab is near Sadr City, the Shiite slum in northeastern Baghdad that was the stronghold of Sadr's militia and the special groups until U.S. and Iraqi forces took and held its southern section after extremists attacked government checkpoints in April and May.

Iraqi forces later pushed into Sadr City proper under a ceasefire agreement with Sadr and promptly began mopping up holdout extremist cells.

The market Echo Company patrolled was a crowded and sprawling mix of single-story shops and stalls selling everything from fresh food to small appliances and sundries.

Rollheiser said his first inkling that extremists were attempting to infiltrate the market area neighborhood to escape the Iraqi Army mop-up in Sadr City came from watching residents during "population engagement" missions.

People who earlier would come up and chat openly with the Americans suddenly started showing more reserve -- hesitancy -- in their public interaction. People, he thought, were again afraid of who was watching.

Echo Company soldiers passed out fliers in Arabic in the market appealing for information about suspicious activity. Other leaflets had photographs of wanted terrorist suspects. Both had hotline telephone numbers to Iraqi security forces and coalition troops.

Rollheiser also made great fanfare of looking at a photograph in his hand and then peering intently at the shoppers and stall owners. Occasionally he'd show it to someone and ask, "Anyone see these guys? They're criminals, they blow up children. We want them."

Rollheiser obtained the photograph during an earlier raid on a home of an extremist gunman. The home had been disclosed by a Sons of Iraq volunteer neighborhood guard. The picture showed four men relaxing outside a hookah shop.

Rollheiser knew the odds of someone knowing one of the men and telling where he was last seen were slim, but holding the picture and then scanning faces in the crowd would get the word out that the Americans were not just looking for Mahdi Army and other insurgents but were looking for specific ones and had photographs of them. Pressure, he said, was the name of the game.

Rollheiser left the market with directions to the hookah shop. It would be visited and then watched.

A "cordon and knock" patrol of a neighborhood later that evening by Echo Company netted at least five illegal AK-47 rifles and several tips about suspect houses. (Although Iraqis are allowed one AK-47 per home by Iraqi law, those who live east of the Tigris River in Baghdad are not.)

Other units from COP Callahan are equally busy doing "population engagement" while performing other tasks. Delta Company recently researched an industrial area where they previously found explosives and bomb components, then handed out fliers in a nearby neighborhood as they scouted out open spaces for a possible park-building project.

Civil affairs officers regularly visit markets and business districts to speak to the people about grants to help create jobs. Other units patrol the streets with Iraqi security forces in the lead or give advice on operations and procedures.

"It a more secure environment" but extremists are still present and the troops remain on guard, an American commander said.

And well they should. A Humvee from Delta Company struck an IED one evening last week while on patrol. There were no injuries, but the vehicle was damaged.

On Sunday, a pipe bomb was found placed near the main entrance to COP Apache in Adhamiya and an IED was found in a pile of garbage elsewhere.

"We've got five months to go before we head home," Rollheiser told his men before a mission. "This is not the time to get bored. This is not the time to get sloppy."