Lt Malcolm was a good chess player. He looked like any other young marines officer: skinny, shaven-headed, although with a quite beaky nose. Anyway, you could always pick him out. He would be the one with the chess board placed on an up-ended box of MREs (Meal Ready to Eat), working out moves. I got to know him a little bit, as his bunk was opposite mine. I would watch as he gave chess tips to those of his men who had not completely given in to poker or hearts. About five hours into the battle, Lt Malcolm was killed.
He was the weapons officer in Alpha Company, 1st Battalion, 8th Marine Regiment, the unit I had joined as an "embed". Just before dawn, Alpha Company blew a large hole in an outer wall, and entered the police station right in the heart of Falluja. It was still pretty quiet then but as the sun rose the marines found themselves surrounded and under attack from all sides.
Lt Malcolm's squad went up on to the highest roof top they could find - but not higher than the two minarets on either side with snipers. There was a wall about 40cm (16in) tall for cover. Everyone tried to get close to it while bullets skipped across the paving stones. When he heard his men were in trouble - the men he'd been giving chess tips just the day before - Lt Malcolm came to get them.
As he ran onto the roof, one of the sniper's bullets hit his helmet, bouncing off. He kept going, and did not leave until he had shepherded all his men down. He was killed by the second bullet. It got him in the back, just below the flak jacket, as he jumped down the stairwell. He must have thought he was home free.
There was no hint of his extraordinary valour in the press release issued two days later. It said: "The Department of Defense announced today the death of two marines who were supporting Operation Iraqi Freedom."
"1st Lt Dan T Malcolm Jr, 25, of Brinson, Ga, died Nov 10 as a result of enemy action in al-Anbar Province, Iraq." The other dead marine in the press release was a Sgt David Caruso, who was not from our unit.
At the end of the day on which Lt Malcolm was killed, the 1/8 had taken between a quarter and a third of the killed and wounded for the entire force, across the entire operation. That was about five times their proportion of the attacking troops.
On Monday, the number of deaths for coalition forces stood at 51, with some 450 injured. These figures represent the coalition's worst losses in any battle in Iraq since the invasion. And the 1/8 still have 20% of those losses.
Lt Col Brandl, the 1/8's commander, came striding across the roof top, wearing wrap-around shades and a broad grin. A cigar was sticking out of one side of his mouth. Everyone else was moving around bent double. The marines called this building "Fort Apache" since in any particular direction you cared to look, someone was attacking them.
"What's our situation, Colonel?" I asked, a little nervous.
"Our situation is good," he said, pausing for a volley of gunfire. "The enemy is coming to us. And we're killing him." Col Brandl's insouciance as he strode around the battlefield - his battlefield - was a calculated act of leadership, designed to steady the nerves of the young marines around him.
I also detected a sense of relief in him. The planning was over. What would happen, would happen. It was up to his marines now. We had got a hint of the enormous stress on Brandl during the eve-of-battle briefing. For three hours, he and his men pored over slides stamped "Top Secret" and walked around a map of central Falluja drawn with marker pen on the floor of their operations room.
Our camera zoomed in close on Col Brandl while he was deep in thought - almost invading his privacy despite this being a very public space. We could see an insistent twitch below his right eye. He had had no sleep for a week and held the lives of hundreds of Americans and Iraqis in his hands. So he would look at a captain pointing a stick at the map on the floor and say things like: "I see an enemy vehicle laden with explosives coming up one of those routes.
"He's going to run one, two, four, five, however many he wants to, right into your flank.
"Once you've got that area isolated, the enemy is yours. It's coming in on your flanks I'm concerned about."
Col Brandl had a good turn of phrase for us journalists. This was one which got widely quoted: "You've got to remember, gents, that this enemy does not like to show his face.
"A lot of the marines that I've had wounded and killed over the past five months have been by a faceless enemy. But the enemy has got a face.
"He's called Satan. He's in Falluja. And we're going to destroy him."
But to his officers in the briefing he said: "There's nothing out there that will defeat us." Pointing to his head, then his heart, he went on: "What our marines, soldiers and sailors, and the Iraqi forces that we have with us, have going for them is not only what's up here [head], but what's in here [heart]. ... "This is a right fight for us, this is a good fight for us. And we're going to win it. And we're going to do it with professionalism and honour."
Lt Bahrns was one of the young officers in the briefing. When I asked about the massive amount of firepower the marines would bring to bear on Falluja, he said: "If there are civilians in there, they are non-combatants, then by no means do we want to hurt a woman or a child. "We're here to protect them, we're here to keep them safe and we're here to turn over Falluja back to them. It's just shoot the bad guys and take care of the civilians."
Lt Bahrns was leading a squad responsible for clearing the insurgents out of the very southern tip of Falluja. It was by now more than a week into the battle, the longest continuous period of urban, house-to house fighting since the Vietnam war.
Alpha Company were holed up in a house right on the edge of the desert. You could really see that the insurgents had nowhere else to go. Every night, though, the insurgents would attack, waiting until just after dark. Half an hour after sunset the first rocket propelled grenades made yellow streaks across the sky, and exploded just behind us.
The marine snipers would try to pick off the insurgents circling around the building. The next morning, we saw their bodies, splayed out at odd angles, already starting to bloat, the flies thick on their faces.
Lt Bahrns told me he had lost his machine gunner. The gunner had been first into a house, the lieutenant explained, and been shot and killed by those inside. The heavy gun was then pulled off the marine's body, and used to fire on the others in the squad outside the house.
There was a long battle. For three hours they could not even get the dead marine's body out. When the marines finally stormed the house, they found three other bodies inside, each holding weapons: two men, and a boy, "maybe 10 years old". You could tell that Lt Bahrns was sickened by this, almost in anguish. "They were shooting at my marines," he said. "What could we do?"
Throughout this entire week, we caught only two glimpses of civilians. One was a group with white flags running away. Another was a shell-shocked man who was brought into the marines' base on a stretcher after being found wandering the streets.
The marines saw many dead bodies - often being gnawed at by dogs in the streets - but they were all of fighters, even if in this one case the "fighter" was a child.
Paul Wood was embedded with the 1st Battalion of the 8th Marine Regiment during the battle of Falluja. His film was shown on Newsnight on BBC Two on Wednesday 24 November.