The Peshmerga have been successfully fighting Isis, driving them back from the gates of Erbil and, with the support of Kurds from neighbouring Syria, re-establishing control over parts of Iraq's northwest.
But they are doing so with a makeshift armoury. Millions of dollars-worth of weapons have been bought by several European countries to arm the Kurds, but US commanders, overseeing all military operations against Isis, are blocking the arms transfers.
One of the Kurds' core complaints is that the Iraqi army has abandoned so many weapons in the face of Isis attack, the Peshmerga are fighting modern American weaponry with out-of-date Soviet equipment.
At least one Arab state is said to be considering arming the Peshmerga directly, despite US opposition.
The US has also infuriated its allies, particularly Saudi Arabia, Jordan and the Gulf states, by what they perceive to be a lack of clear purpose and vacillation in how they conduct the bombing campaign. Other coalition members say they have identified clear Isis targets but been blocked by US veto from firing at them.
"There is simply no strategic approach," one senior Gulf official said. "There is a lack of co-ordination in selecting targets, and there is no overall plan for defeating Isis."
Britain is moving closer to expanding its role in the war.
The Government yesterday gave its strongest indication yet that MPs will be given a new vote on whether to bomb Isis in Syria.
Michael Fallon, the Defence Secretary, said it was "illogical" that British planes were able to hit extremists in Iraq but not across the border.
Any decision to bomb in Syria would have to be approved by MPs.
Isis' Egyptian affiliate has claimed responsibility for a wave of deadly attacks in the northern Sinai Peninsula on Wednesday night that killed dozens of soldiers.
The extremist group, known as Sinai Province, claimed it had launched 15 separate attacks, including two car bombs, in the towns of Al-Arish and Sheikh Zuwayid, near Egypt's border with Gaza and Israel.
It was Isis' deadliest attack on Egypt to date.