But the largely overlooked presence in Syria of growing numbers of Iraqi Shiites, battle-hardened veterans of Iranian-backed militias that fought the Americans, underlines how Tehran is forming a "foreign legion" that's spreading across the troubled region.
As the war drags on, Iran is reported to be taking an increasingly active role on the ground through the elite covert action wing of the Islamic Revolutionary Guards Corps, the al-Quds Force.
This organized, trained and armed Iraq Shiite groups to fight Americans during their eight-year occupation of Iraq that ended in December 2011.
There have been constant reports that units of the al-Quds Force are in action in Syria.
These have not been confirmed, but the February assassination in Syria of Brig. Gen. Hassan Shateri, a senior al-Quds officer who'd been based in Lebanon for years working with Hezbollah, indicated the level of active support Damascus is getting from Tehran.
Shateri, an experienced covert operator, was accorded a high-profile military funeral in Iran. That's unusual for officers who operate in the shadows and indicates that Tehran's involvement in Syria is now so extensive that it's not bothering to mask it anymore.
Michael Knights, an expert of Iran with the Washington Institute for Near East Policy, estimates there are currently as many as 2,000 Iraqi fighters in Syria.
These men, veterans of the Iraq conflict, like Hezbollah's battle-seasoned operatives who've fought Israel for 30 years, have become key elements in Syrian President Bashar Assad's forces as they engage in a new offensive against largely Sunni rebels around the northern city of Aleppo.
Knights says "one of the most significant international brigades" under Assad's command is the Liwa Abu Fadl al-Abbas based in Damascus, which is predominantly made up of Iraqi fighters organized and supported by the al-Quds Force.
"Though relatively small in size, LAFA could have a strategic impact on the war's course," he observed in a June 27 analysis for the Washington Institute.
"More broadly, its expansion marks a potentially dangerous turn for the region, giving Tehran a transnational Shiite militant legion that it could use to bolster its allies outside Syria."
These fighters are "almost exclusively" drawn from three Iraqi groups that were creatures of the al-Quds Force and its enigmatic and powerful commander, Maj. Gen. Qassem Suleimani, during the U.S. war in Iraq.
Hezbollah, Iran's prize proxy in the Middle East, was called in to train these fighters in 2006 and pass on the lessons it learned fighting the Israeli army.
A key figure in that operation was Ali Musa Daqduq, a veteran Hezbollah commander. He operated with a Shiite group called Asaib Ahl al-Haqq -- AAH, or League of the Righteous -- and was captured with several of the group's leaders by British Special Forces in Basra in southern Iraq March 20, 2007.
The Americans wanted him on charges of killing U.S. soldiers, but he was held in Iraqi custody. After U.S. forces left Iraq in 2011, the Central Criminal Court released him on the grounds of lack of evidence, clearly at the behest of Tehran despite a U.S. extradition request.
Given his expertise in guerrilla warfare against Israeli and U.S. forces, and running irregular forces, it's possible Daqduq's back in action in Syria.
Knights says AAH is one of the Iraqi groups that contributes men to LAFA. The others are Ketayeb Hezbollah, an elite, 400-man cadre of experienced Iraqi Shiite fighters who report directly to the al-Quds Force command.
The third is Ketayeb Sayyid al-Shuhada, a 200-strong force led by Abu Mustafa al-Sheibani, aka Hamid al-Sheibani, a veteran covert operator who Knights avows has worked under the al-Quds Force since the late 1980s.
AAH and Keyateb Hezbollah, Knights says, "are apparently streaming fighters to Iran and Lebanon to be retrained for intervention in Syria.
"Specifically, they have been taught how to move from the insurgent tactics used in Iraq to the urban street fighting and conventional military skills required for regime security operations in Syria -- skills that could also be used in Lebanon or even Iran if needed."