By Jonathan Marcus
BBC diplomatic correspondent
One of the most enduring images of the Vietnam War is that of the last American helicopter lifting off from the roof of the US embassy in Saigon, in April 1975.
The Vietnam war divided a generation of Americans
The shaky ladder up to the last point of escape somehow symbolised the fragility of America's position in the world.
This was certainly how it looked to Leslie Gelb, now President Emeritus of the prestigious think-tank, the Council on Foreign Relations in New York, but then a senior Pentagon official.
"That image," he told me, "looked like the ultimate symbol of America's defeat. It looked like the beginning of America's strategic demise in the world."
The Vietnam War certainly divided a generation of Americans. But it did not lead to the collapse of American influence that Leslie Gelb feared.
Skilful diplomacy and a world still chilled by the Cold War helped the US to manage the consequences of its defeat. So Vietnam had dramatic and lasting implications at home but only limited consequences abroad.
Re-building from scratch
A series of discussions in Washington suggests that the current conflict in Iraq will be quite the opposite - limited consequences at home, but a dramatic and lasting impact abroad.
The military in Iraq is already having to re-learn some of the lessons of Vietnam.
And this is strange in a way, since so many of America's senior commanders remember joining a military that was deeply marked by the Vietnam experience.
The current US commander in Iraq, General David Petraeus, is a case in point. He was in high school during the 1960s and watched the tail-end of the crisis from the US Military Academy at West Point.
By the time he was posted to his first unit, America's fighting war was largely over.
But, speaking from the US embassy in Baghdad, he told me that the army he joined was beset by problems - drugs, indiscipline and the loss of experienced non-commissioned officers.
"All of the pillars of a professional force had to be re-built from scratch," he said.
The generals were also determined that they would never have to fight a war like Vietnam again. They returned to the type of warfare they believed America understood best - equipping and training for high-technology armoured combat against the Soviet Union.
A so-called "Vietnam syndrome" afflicted the conduct of US foreign policy for over a generation - a reluctance to use force and an understandable conviction that if America was going to go to war again, then it would have to do so with the full support of the American people.
US forces have a new manual for counter-insurgency warfare
As Dr Conrad Crane, director of the US Army's Military History Institute told me: "Such wars would have to employ massive force -there would be no more of these small conflicts with uncertain goals where the US seemed to be tying its hands behind its back."
The man responsible for thinking again about the lessons of Vietnam is General Petraeus.
He instituted a new manual on counter-insurgency warfare for the US military. It was in large part written by his former class-mate, Mr Crane! And it is this manual that provides the theoretical under-pinning for the current surge operations in Iraq.
I went to see Lawrence Korb, a former assistant secretary of defence in the Reagan administration and now a thoughtful researcher on things military.
"The way in which we have used the army in Iraq," he told me, "is unprecedented certainly in the period since the end of the World War II."
Unlike, for example, the British Army, that sends its troops to serve six-month tours of duty in combat zones, many US personnel serve up to 15 months at a time and many are on their third deployment to Iraq.
This, Lawrence Korb says, is creating massive social problems in the military - divorce rates are up, suicides are up. This overstretch, he says, "is probably going to take a decade to fix".
The strain on the US military is matched by the strain on America's image abroad. Opinion is strongly negative even in countries that are close allies of the US.
So what does all this mean for the coming presidential election?
Iraq looks set to remain a central issue. In many ways it is a code-word for a bundle of assumptions about America's relationship with the outside world.
And the outside world will be watching this election very closely.
Indeed, I came away from America with the view that the importance of this election cannot be overstated.
For a final verdict, I turned to veteran political observer David Gergen, a man who served four presidents, both Republican and Democrat.
"The challenges facing whoever enters the White House in January 2009 will be immense," he told me.
"In my judgement," he went on - acknowledging that what he was going to say might sound overstated - "the next president of the United States is going to face the toughest set of problems of any new chief executive since Franklin Delano Roosevelt took office in March 1933, in the midst of the Great Depression."
The second programme of the Seeing Iraq: Thinking Vietnam two-part series will be broadcast on Monday 3 December at 0800 GMT on the BBC World Service.