It may be hard to believe, but it's perhaps becoming more important than ever that US forces find Saddam Hussein, or incontrovertible evidence of his death.
As attacks on US troops in Baghdad mount officials in Washington are increasingly worried that Hussein has become a symbol used by remnants of his regime to rally their supporters.
Fear that Hussein may be coming back could now be intimidating Iraqis otherwise sympathetic to US goals. Baath Party elements have already expanded their targets to include police cadets, utility officials, and others deemed too close to American civilian administrators.
US officials are now going so far as to flatly state that if Hussein remains alive he will be found and brought to justice. That marks a toughening of official rhetoric - in the past, most in Washington said their target was a regime, not a person.
"Finding the leadership element, which was what the whole war was about . . . is still the key to the postwar phase," says retired Brig. Gen. John Reppert, an expert on military strategy at Harvard's John F. Kennedy School of Government.
Administration officials continue to insist that the resistance encountered by US troops in Iraq is not the work of a nationally organized force.
A disparate array of groups are likely the source of the violence, they say. These include Baath Party political loyalists, Fedayeen Saddam guerrilla groups, and international terrorists.
Some of these terrorists "have connections to Iran," said L. Paul Bremer, the top US administrator in Iraq, in a Baghdad briefing July 1. "Some have connections to Al Qaeda. Some are from other countries in the region."
Whatever their source, the attacks have begun to take a steady toll of casualties.
At time of writing on Monday, three American soldiers had been killed over the previous 24 hours.
Early Sunday one GI was shot point-blank as he walked through Baghdad University, whose southern Baghdad campus had been considered a relatively safe area.
Then on Monday gunmen ambushed a US platoon in northern Baghdad's Adhamiyah neighborhood, killing one. Later a homemade bomb tossed at a US convoy in roughly the same area of the city killed another American service member. Also on Monday, in the town of Ramadi, 60 miles west of Iraq's capital, someone fired a rocket-propelled grenade (RPG) at another US convoy. Four were wounded.
Whether these attacks are directed by some central authority or not, they have the effect of undermining American authority, says military expert and retired Air Force Col. Sam Gardiner.
The rapid American invasion of Iraq and the quick ascension of US power in Baghdad created an aura of overwhelming strength. Perhaps inevitably, that aura has now been tarnished.
"A small number of attacks showed that the Americans were vulnerable," says Gardiner.
The sheer number of attacks, combined with their widening geographical spread, has reportedly raised fears among many Iraqis that Hussein is not gone for good after all - and perhaps, just perhaps, may be able to outlast US patience and regain power.
Horrific assaults against Iraqi police cadets and others whose work necessarily brought them into close contact with US officials have only added to this sense of foreboding.
"I think people are scared to death," says Judith Yaphe, an Iraq expert at the National Defense University. "Remember, it's not as if they saw Saddam everyday anyway - his absence doesn't mean a lot."
Thus a ruler who made his authority mysterious by appearing only intermittently while in power can remain in his subjects' minds even after his disappearance.
The nature of some of the attacks on US forces indicates that some organized elements of the Saddam regime have survived, says Ms. Yaphe.
While some of the attacks are simply criminal assassinations, others have required stealth and the use of RPGs and other heavier weapons, reflecting a level of training available only to Fedayeen Saddam or other regime remnants.
If Saddam is still in charge, he could be directing these groups to run amok in an attempt to destroy a country he can no longer have.
That is what he did in Kuwait, after it became apparent that the Gulf War would oust him from the country. Iraqi forces burned and looted as they retreated north.
Or he could genuinely harbor hope of regaining his power. Perhaps he calculates that a steady stream of casualties will quickly cause the American public to turn on the Iraqi effort.
"Saddam's trying to replicate Vietnam," says Yaphe. "He's always been taken by this concept of Vietnam.... He saw that when the body bags started coming home, the war ended."
In any case, Saddam himself may be even more of a US target now than he was when the Iraq war began. The announcement of a $25 million award for his capture or hard information proving his demise shows how much US officials now believe that they must erase his value as a symbol to hard-core resistors.
US rhetoric about Saddam has now ratcheted up to the point where it may risk being counterproductive.
"Sooner or later, we'll get ya," said L. Paul Bremer last week, mimicking the tough-guy rhetoric of President Bush.
It is still possible that Hussein was killed in airstrikes during major war operations. But Sen. Pat Roberts (R) of Kansas, chairman of the Senate Intelligence Committee, told CNN Sunday that there is a 70 percent chance Hussein is alive. "It is a big-ticket item for us if we're going to eliminate the fear and be successful.... We have to kill or capture Saddam and his two sons."