Then-Army Brig. Gen. H.R. McMaster addresses cadets at the National Military Academy of Afghanistan, in Kabul, on Dec. 7, 2011. He is one of the U.S. military’s general officers credited with affecting positive change in Iraq during the U.S. war there. (U.S. Army photo by Sgt. Tamika Dillard)

The U.S. military last week selected Army Maj. Gen. Dana Pittard to lead U.S. operations in Iraq as security there continues to deteriorate. As the deputy commanding general of the Army’s force based in nearby Kuwait, he was seen as a logical choice; Pittard had previously deployed to Iraq both as a brigade commander in the early part of the war and as a brigadier general who oversaw U.S. adviser teams there in 2006 and 2007.

There’s a call for more involvement by some of the Iraq War’s most famous U.S. generals, though. U.S. Rep. Duncan Hunter (R.-Calif.) sent a letter to Defense Secretary Chuck Hagel on Monday, saying he should bring up for re-assignment a number of officers who had key roles in Iraq in 2007 and 2008, as the effects of the U.S. surge and the Anbar Awakening began to take hold and violence there waned. Hunter’s suggestion followed a fiery call Sen. John McCain (R.-Ariz.) made June 13 for President Obama to fire his entire national security team and consult with retired Gen. David Petraeus, the architect of the surge.

Hunter says Petraeus should serve as a liaison to Iraqi Prime Minister Nouri al-Maliki. But he also focuses on lower levels of command, highlighting individuals who aren’t nearly as famous as Petraeus or Marine Gen. James Mattis, who retired last year as perhaps the most popular general of his generation. The others he named include:

Marine Gen. John Kelly — Hunter cites the trust Kelly built with tribal leaders in Iraq’s western Anbar province as potentially helpful now. Kelly, now the four-star commander of U.S. Southern Command, was the two-star commander of Multinational Forces-West in Iraq from February 2008 to February 2009. He has been promoted twice since, and was seen as a possible candidate to become the next commandant of the Marine Corps before Gen. Joseph Dunford was nominated for the job.

Army Maj. Gen. H.R. McMaster — In listing McMaster, Hunter names one of the most interesting and controversial generals of the war. He was a colonel under Petraeus and was bypassed for promotion to brigadier general until Petraeus himself got involved in the process in 2008. McMaster was later chosen to serve as a top planner for Petraeus after he was selected to lead U.S. operations in Afghanistan. More recently, he has served as the two-star commander of Fort Benning, Ga., and its Maneuver Center of Excellence, which leads research on how to make ground forces the most effective. He was selected to pin on a third star in February.

Army Maj. Gen. Sean MacFarland — As a colonel, MacFarland led U.S. troops in 2006 and 2007 in Ramadi, a western city with a fierce insurgency. He adhered closely to the counterinsurgency principles Petraeus and other senior officer embraced. Violence eventually subsided, and MacFarland’s career has been on the rise ever since. He is now the two-star commander of the Army’s 1st Armored Division and Fort Bliss, Tex., where he replaced Pittard in 2013.

Marine Col. Dale Alford — He served as a battalion commander in Iraq in fierce fighting in Anbar in 2005. More recently, he oversaw Marine officer training at The Basic School in Quantico, Va., and at the Pentagon in the Plans, Policies and Operations division. He was nominated to pin on his first star in February.

Marine Col. William Jurney — Like Alford, he was a battalion commander in Iraq in 2005. More recently, he has served as an executive officer to Dunford, the top commander in Afghanistan, and was nominated to pin on his first star in February.

Other officers that Hunter named, like Col. Mike Shupp and Col. Joseph L’Etoile, have since retired. Nevertheless, Hunter includes them on a list of “old hands” that should be called back to help. He also leaves off some strong options, like Marine Maj. Gen. David Berger, who was a regimental commander in Iraq in 2005 and has since served as a division commander in Afghanistan. He was nominated to pin on his third star and lead I Marine Expeditionary Force, of Camp Pendleton, Calif., in May.