"You can put a shoe in the oven…

...but that doesn't make it a biscuit."

Malcolm X

"I have some news. Al-Qaida is in Iraq. It’s called ‘al-Qaida in Iraq.’”

John McCain

As Professor Cole explains (my emphasis)...

The technical definition of al-Qaeda is operatives who have sworn fealty to Usama bin Laden. There were only a few hundred of them. I doubt whether more than a handful of such individuals are in Iraq.

So there isn't any "al-Qaeda" in Iraq in the technical sense. There are "Excommunicating Holy Warriors" (Takfiri Jihadis), i.e. devotees of political Islam who are violent and willing to deploy terror for political purposes. They declare other Muslims who disagree with them "not Muslims,"-- thus the "excommunicating" bit. But there are only a few hundred foreign fighters. A small minority of Iraqis has associated with them. They don't call themselves 'al-Qaeda in Iraq.' The major such group is "The Islamic State of Iraq." And to say that they have "bases" in Iraq is pretty grandiose. They have some safe houses and try to take and hold neighborhoods, so far with indifferent success.