But the Syrians are still sending jihadis into Iraq, even though the flow is much reduced. This flow is enough to sustain bombing attacks on occasion in Baghdad and especially in Mosul:
Officials in Iraq's third largest city, Mosul, have warned the terrorists will not be defeated until the border is secured.
Iraq has deployed extra troops, including two brigades of the paramilitary National Police, into the battle for the northern Sunni Arab city, but the effort has been handicapped by widespread infiltration of the security forces by terrorist sympathisers.
Dureid Kashmula, the provincial governor, said: "One of the reasons that al-Qaeda is so strong here when security is improving across Iraq is that the terrorists can come across the border.
"So the number of security forces is never enough to defeat the threat."
Nineveh, the province surrounding Mosul, has a 227-mile border with Syria.
Mosul's continuing turmoil barely registers outside the country. Even visitors to the city of 1.7 million view it as a distraction from the overall picture of falling violence in Iraq.
Khosro Goran, the vice-governor, said: "We have an open border with Syria and our neighbours are actively encouraging the terrorists.
So be very clear, our presence is still needed. I have been tempted many times over the last year to declare victory. Even though other writers have done so, I refuse to commit. We are winning, that is clear. But as long as enemies fight the war is not absolutely won.
This fight in Mosul could be the last gasp of al Qaeda in Iraq if we can help the Iraqis to defeat the jihadis and cut off the supply of new killers coming in from Syria.
Or, if we pull out too fast, this could be the nucleus that allows the jihadis to spread throughout Iraq again with increased support from Syria. And Iran can then jump in again with two feet to support Shia killers and finally get that bloody civil war that Syria and Iran desperately want in Iraq.
The stakes are high. No amount of hope can change that simple fact.
