Going into places like Fallujah and taking control is not as much of a problem. Keeping control is difficult, because the current government has a bad case of "the Iraqi disease." This affliction causes Iraqi politicians to believe their troops and police are more capable than they are. Although Saddam had this problem when facing foreign armies, he had a better sense of proportion when it came to terrorizing his own people. The current government is willing to just put civilians into police uniforms, give them a week or two of training and put them on the streets. American commanders are having a hard time pointing out the obvious; that this doesn't work. The cops and troops require more training, and the officers even more so. The Iraqis like to believe in magic, and have a hard time admitting that magic doesn't work.  Saddam's followers don't believe in magic, they believe in terror, and terror does work.