Travis Patriquin wrote a pretty in-depth explanation about the difficulties fighting the insurgency. His earlier, more famous PowerPoint slide gets to the point quickly and humorously. This article was recently published in The Military Review (Hat tip: Mr Patriquin and Matthew B).
Based on my own experience downrange, and the experience of some of my Airmen who were deployed with special forces, I tended to marginalize "Former Regime Elements" in favor of wanting to go bash the Jayesh al Medhi and the foreign fighters. It looks like I wasn’t giving the Saddam loyalists their due for the trouble they’ve caused in Iraq.