It was, I heard the loadmaster's voice shouting in my headset, the worst time of day to be flying a helicopter. Just after five in the afternoon, the Baghdad sky was darkening for the night.
Large parts of Baghdad are unsafe for coalition forces
Half an hour earlier, the visibility would have been perfect. Half an hour later, the pilots would have used their night-flying goggles.
So would the loadmaster, who was also in charge of the two big machine-guns pointing out of the helicopter's open doorways.
"Low height," said an unnaturally calm voice in my headset, sounding like a prefect from an English girls' school.
It was the Puma helicopter's talking warning-system. And the helicopter was a Royal Air Force one. How the voice would sound if we were about to crash, I don't know. I imagine she would have been her prim self, collected but slightly reproving, as though the pilot should never have got himself in that position.
From below, military helicopters always seem threatening and all-seeing. If you have been hunted by one, as I have, you feel the pilot knows exactly where you are and is just playing with you before he destroys you.
Up here, though, the position seems entirely different. You feel intensely vulnerable. "Got to watch out," the pilot said to the co-pilot over the intercom, perhaps not realising I was listening.
"Very easy to miss a high-tension cable when it's this dark."
Saddam on trial
British military helicopters fly at only 40 metres above the ground in potentially hostile areas like Baghdad. American ones fly twice as high, at around 80m: much safer from high-tension wires, but much less safe when it comes to fire from the ground.
"They're always taking hits," the loadmaster shouted to me. "We very rarely get any."
Low-flying helicopters may be safer from ground fire
I understood why. A low-flying helicopter makes a huge racket, but it is overhead and gone before anyone has time to take a pot-shot at it.
Our helicopter was taking us from Baghdad international airport to the Green Zone for a report we were making for BBC News. It flew fast and purposefully, and it was only eight minutes before we saw ahead of us the cross-swords of Saddam Hussein's old victory monument, dating from the time of his war with Iran.
In point of fact it wasn't a victory at all, and his unprovoked decision to invade Iran is one of the crimes the special court will soon try him for - after his present trial, for the murder of 148 Shia men and boys in the town of Dujail in 1982.
He will presumably defend himself by pointing out that the Americans and British, who later overthrew him, were only too happy that he invaded the newly established Islamic Republic of Iran, following the overthrow of the Shah - Britain's and America's ally.
Maybe Britain and America dropped a hint that they wanted him to invade? If so, we will certainly hear about it in court during the weeks ahead.
Other embarrassing things have already come out, though not yet at Saddam's trial. Documents recently leaked to the Daily Mirror in London, and now blocked from further publication by a gagging order from the British government, indicate a serious disagreement between Tony Blair, the British prime minister, and his friend President George W Bush last year.
Much has been made of Mr Bush's apparent suggestion about bombing al-Jazeera TV's studios, which may just have been a joke. More important was the difference of opinion over the fighting in Falluja, west of Baghdad.
In April 2004, US marines staged a ferocious onslaught on the town, on orders which apparently came direct from the White House.
The resistance was intense, and spread across Iraq. According to the leaked document, Tony Blair was worried that the backlash might drive the coalition forces out of Iraq altogether.
The resistance movement has gone from strength to strength ever since the attack on Falluja, and though Tony Blair was wrong to think it might drive the coalition out immediately, the Americans and British have been on the defensive ever since.
Neither he nor President Bush would be considering a quick withdrawal from Iraq now if the resistance hadn't been so effective.
Still, as our helicopter flew over the road from the airport to the centre of town, there was one success the Americans could claim here.
Six months ago, that road was the most dangerous in the country, with car bombs going off virtually every day.
Now there are scarcely any attacks at all. The Americans have brought in Iraqi soldiers, who check every vehicle.
Yet the overall level of violence in Baghdad has scarcely been affected. The bombers have headed elsewhere, to find easier targets.
As we came down over the Green Zone, the loadmaster pointed to the far bank of the Tigris River. "That's bad guy territory," he shouted. True enough, but large parts of Baghdad now qualify for that description.
American accents over the radio guided our helicopter in to land.
"Low height," the prefectorial voice warned again as we came down. A jolt, and I was in the Green Zone - just about the one really safe place left in this city.
Do you agree with John Simpson's view that the Coalition forces in Iraq have been on the defensive since Falluja? Just how far has Iraq become "bad guy territory" in the past year?