This is little off track but maybe useful. In police world we use the problem/crime or disorder triangle. That is our Holy Trinity. They could also be thought of as centers of gravity. I will try to translate this into COIN ops.

It starts with what is called a problem or crime/disorder triangle.
It has three COG's
1-a motivated offender (insurgent)
2- an accessible target/victim (vulnerable population or physical thing,oil well)
3-a hot spot location(failing or failed state, nobody in charge).

If you are teaching this to Bubba it is called the wolf,the duck and the den. All three must be present to have a crime or disorder problem happen.

To collapse the triangle, you can:
1-arrest the wolf
2- protect the sitting duck
3-clean up the den so it doesn't attract future wolves.
In the worst case you may have to do all three at once but often they can be done one at a time. the COG may shift during your operation depending on how effective you are and the general situation. No one technique works everywhere or all the time. Criminals are very adaptive.

The Iraq parallel:
1-An Bar is a wolf problem or wolves, you have several wolf packs and until you deal with this nothing much will change.
2- Baghdad is a duck problem (sitting ducks) vulnerable population. To fix this you need boots on the ground and eyes in the sky.
3-Iraq in general is a den problem a failing state with valuable targets (oil) that will attract a lot of wolves. To make it worse you have problems with the internal infrastructure (elc.,water,jobs,etc.) poor den keeping.

In summary Iraq is about the worst problem you could have, but it could be solved by applying the outer control triangle, if we wanted to. But that would require a whole other post so I will wait on that.