Don't fret, just widen your mind and remember that the Iraqis surrendered by the hundreds of thousands to us back in 1991 when they KNEW that Saddam was still alive, so they aren't likely to have much more fight in them now (especially if they hear so much as a rumor that he's dead or seriously wounded).
Oh, and also remember that we can control the radio and TV anytime we desire, to tell them whatever mush needs to be in their heads at the right moment.