In some wars, that merely means destroying a conventional army. However, as in this case, the irregular forces must also be destroyed.
It is folly to speak of the winning hearts and minds of these irregular forces any more than it would be to speak of winning the hearts and minds of a German SS Division.
They have to be killed.
The Iraq War was not "won" when that statue of Saddam fell one year ago. The war will not be won until Saddam's irregular forces are isolated and killed. Fallujah is a start but there may be other Fallujahs.
Saddam's irregular forces are no match for the U.S. military and they have no hope of defeating the U.S. military on the battlefield.
However, Saddam's irregular forces have a very real possibility of defeating the U.S. by striking at America's Achilles' Heel which is the morale American Home Front.
Let's face it. Compared to the to the American Home Front of 1944, the American Home Front of 2004 has the backbone of a chocolate eclair.
In their corner, Saddam's irregular forces have the American liberal news media and the Democrats who have a common goal of undermining the resolve of the American Home Front.
The Iraq War will be won or lost in a race between the U.S. military's efforts to kill Saddam's irregular forces and the efforts of Saddam's irregular forces, the American liberal news media and the Democrats to convince the American Home Front that America has lost the Iraq War.