The most difficult thing was the noise. As the engine roars hour after hour, an amphibious assault vehicle feels as if there's a juggernaut in your head. Even at night, when we slept, huddled on a wooden pallet balanced between the benches lining each side, the marines would keep cranking the engine.
There were bangs, thuds, crashes, crackles, whooshes - all the comic book words you can think of to describe the noises of war. Mortars, small arms, aerial bombs, tanks, rounds, artillery, missiles, detonations. It didn't stop for ten days.
All the time, I was thinking: why are they letting us do this? While the British military assume that journalists are there to catch them out, and must therefore be kept at bay, the Americans are so confident of the rightness of their mission that they are only too happy to let us report from the front line. They think it's a good thing to show marines blowing up buildings and killing people in Fallujah. And so we did.
Our stories were neither vetted nor censored. We obeyed the ground rule that we should not jeopardise "operational security" by giving away the unit's position or plan; nor could we broadcast images or names of marines killed in action before their families had been notified. Other than that, we were largely given open access.
I sat in the Amtrack and listened to the guys chatting.
"I don't like spray and pray. I like to snipe those motherfuckers. Two shots and he's dead - one in the chest and one in the head."
"I hate this fucking country."
"I keep thinking - why am I here?"
"What I hate is that we have to play by the rules and they don't."
They talked of home - girlfriends, wives, ambitions for college, plans to leave the military. The three marines in the Amtrack never once complained about us cramping their space, nor about our involuntary sabotage of Operation Phantom Fury, by draining the Amtrack battery with our edit gear so they had to jump-start the vehicle.
I was stunned every day by their youth. The driver, who was 21, received an early Christmas gift from his 19-year-old wife. It consisted of sweets in a funny mug and a Spiderman toy, which he proceeded to play with for a short while. When they weren't on duty, they watched South Park on a hand-held DVD player.
The job of the Amtracks was to "lift and cover" - in other words, to carry foot soldiers into Fallujah to fight and to stand guard over their heads as they moved on foot from house to house. The platoon we rode with were lifting India Company of the 3rd Battalion, 5th Marines. The most senior infantry officer was Captain Brian Chontosh, whose exploits in Iraq last year not only won him the Navy Cross for bravery, but also inspired an internet-based computer game. He had a good ear for the soundbite. "We asked them to surrender, but they said they'd rather die. So they're gonna die," he told me, as we stood on a rooftop waiting for the air force to bomb a building his men had been mortaring a few minutes earlier.
Not only did we not see the other side, but we saw only a small slice of the American side because each unit operates in a different area and, if you're on the front line, you can be in only one place at a time. So I don't pretend to know what happened in Fallujah. But I can make some educated guesses by extrapolating from what I saw.
I do not believe the American claim that they killed 1,200-1,600 insurgents. Return fire was sporadic and we saw very few bodies. I suspect most insurgents fled to Ramadi, Mosul and elsewhere.
Nor do I believe those who say that most of the dead were women and children. I went out with a body collection team and all the bodies we saw that morning were male. I do not know whether they were insurgents or civilians who had stayed at home to try to protect their houses from looting.
I doubt that there is a humanitarian crisis in Fallujah now, because so few civilians remained in the city. But I think there will be a crisis soon, as people return to find their houses in ruins and their livelihoods destroyed.
The essential mystery of Fallujah, however, remains unsolved. The marines uncovered evidence of torture chambers. India Company came across a house with five bodies, all male, who had been shot in the back of the head. I have no doubt that terrible people ruled Fallujah, and that the most brutal writ ran there.
So what did the people think? I have no idea, because I have no way to ask them. It is far too dangerous for any foreigner to find out by going to Saqlaweiya, the suburb north of the city where 4,000 families fled just before the assault. We would be kidnapped if we tried. Iraqi journalists are also in danger, and as yet I've seen no article that answers adequately the question - did the people acquiesce to the regime in Fallujah out of fear or did they support it as a "resistance struggle"?
Two soldiers in the "Traks" unit were killed, both from mortars landing where they were standing. They weren't even on the front line, but at Command HQ. Six were injured and medevac'd out. Three men in India Company were killed. (The marines never say "killed" or "dead"; they say "KIA" for killed in action. I suppose it's easier than saying the real words.)
When we got back to Camp Fallujah, I came across a sergeant I had spoken to before the assault. A big, thoughtful African-American, he had read the recent book Battle Ready by the retired US general Anthony Zinni, and expressed amazement that some marines still thought there were WMDs out there.
"The trouble with marines is that they don't read enough. Some don't read at all," he had told me earlier. I asked how he was doing.
"Been better. I hope it was worth it," he said. "I hope it works."
"How will you know?" I asked.
"If the insurgents are defeated," he said. "Otherwise it will all be for nothing. They'll be KIA for nothing."
By being embedded, I saw at close hand how the marines fight. I learnt a lot about the military. But it didn't change my mind about the American intervention in Iraq. I don't think it will work. Nor does the sergeant, but he can't quite bring himself to admit it.
Lindsey Hilsum is international editor for Channel 4 News