The U.S. military will have more than 3,000 troops in Iraq sometime soon, part of an increase  aimed at training up to 45,000 Iraqi soldiers to defend against Islamic State militants. But at least one major element of the Pentagon’s involvement in Iraq is missing so far now: embedded independent journalists.

The modern media embed program in Iraq began in 2003, with 692 journalists embedding during the U.S. invasion of the country that March and the subsequent fall of Baghdad, according to a September 2004 assessment produced for the Defense Department by the Institute of Defense Analyses. The program’s early goals were to dominate media coverage of the war, counter third-party “disinformation” and to nurture U.S. and international support, the report said.

Thousands of journalists have embedded with U.S. troops in Iraq and Afghanistan since. For civilian journalists like me, the assignments provide immersive learning in the dangers that Americans and civilians alike face in war zones, the complexity of military operations and the proud, complicated culture of the service members who carry them out. Embedding can be scary at times, but it also can lead to powerful journalism that explores how a military campaign is going and what the troops prosecuting it think and feel.

In Iraq, media embeds ended when the United States pulled virtually all of its remaining troops out in December 2011. They have not been reestablished, six months after President Obama sent several hundred military advisers to Iraq in June and four months after the United States began launching airstrikes against militants there. Virtually nothing has been heard from rank-and-file troops in Iraq in that time frame.

The small number of U.S. troops in Iraq now is far smaller than what deployed during the wars in Iraq and Afghanistan and makes it impossible for the military to embed reporters, said Army Maj. Curt Kellogg, a spokesman with U.S. Central Command.

“Given these small numbers of U.S. troops, there is currently no capacity to host embeds in Iraq,” he said. “As Operation Inherent Resolve progresses, we will continue to examine ways to best facilitate media coverage.”

A change could be coming, though. Rear Adm. John Kirby, the Pentagon press secretary, said that after the military sets up a new headquarters commanded by Army Lt. Gen. James Terry in coming months to oversee operations in Iraq, media access could improve and accommodate short visits to interview the troops and see what is happening. It’s unlikely that a full embed program will be set up, Kirby said, but it would still be an attempt to provide more disclosure.

“We recognize that this is something that we need to improve upon,” Kirby said.  “It truly does come down to infrastructure,” he added, referring to the helicopters, vehicles and other resources that reporters use alongside the troops in theater.

Kirby said senior Pentagon leaders have discussed “literally from when this first started” in Iraq how to get media access, but there are several challenges to doing so, in addition to the relatively small number of troops deployed.

When the United States included media in its invasion of Iraq in 2003, it was not concerned about diplomatic sensitivities. The U.S. military is there now at the request of the Iraqi government, and officials in Baghdad would have a say in any program adopted, Kirby said.

“It’s still the Iraqis’ war. It’s not the Americans’ war,” Kirby said. “We have Iraqi partners that get a vote here.”

Outside of airstrikes and occasional humanitarian airdrops, the current mission also is “much more discrete” than counterinsurgency, which requires frequent patrolling and tens of thousands of troops providing security while living on small bases among local civilians, the admiral said.

Kirby rejects criticism that the Pentagon is trying to hide what is occurring in Iraq. Not only has the military conducted regular media briefings and released regular updates detailing airstrikes, it has taken journalists on Navy ships and hosted media in Tampa, home to Central Command, he said.

Another senior public affairs officer at the Pentagon, Marine Col. David Lapan, told a room of journalists at the Military and Reporters and Editors conference in October in Washington that while the Pentagon chose to embed media during the Iraq War, they did not believe it would be the best bet to coordinate media coverage in all future conflicts.

The Pentagon has a history of embedded journalists in conflicts with small numbers of U.S. troops, however, including during the initial invasion of Afghanistan. The Institute for Defense Analyses report notes that media were not allowed to accompany Special Operations units involved in the opening salvos of that war in fall 2001, but a handful of reporters were on helicopters with Marines as they flew into Kandahar province from Navy ships in December 2001 and established Camp Rhino. Media embeds became more common in Afghanistan by February 2002.

The military also embedded media during military operations in Bosnia in 1995, with reporters joining units in Germany and spending weeks with them in the field, the report says. It was less common in 1999, when the United States was involved in a military campaign in Kosovo that was conducted primarily by air.

The U.S.-led coalition force in Afghanistan continues to take media embeds, even as American military involvement there wanes. U.S. military officials in Afghanistan warn on their Web site that embeds longer than 24 hours outside of Kabul will not be permitted unless requested and approved by a top coalition commander. But they still occur, with Drew Brooks, a reporter with the Fayetteville Observer in North Carolina, among the most recent to spend numerous days with the troops.