In north-central Iraq, about 80 miles (130 kilometres) north of Baghdad, Kurdish troops are advancing quickly south.
Kurds do not want to upset post-war talks
They have just taken the town of Tuzkhurmato, and another one called Jalula.
These are smallish but significant places on the road which approaches the main Kirkuk-Baghdad highway.
There is an Iraqi division next to the highway, and the fighting is still going on.
'Fighting like devils'
The local Kurdish commander has said the Iraqis are putting up fierce resistance.
He said they are fighting like devils, and he has not seen anything like it in 20 years.
The Iraqi soldiers have had months of propaganda telling them the Kurds will cut their throats if they are captured.
They have been told to fight to the last because a terrible fate awaits them.
When I have seen the Iraqi prisoners in Kurdish hands, they have actually been treated perfectly reasonably.
I think the Kurds have a certain amount of sympathy for them, and that increases as Saddam Hussein falls.
But this news is not getting across.
The assumption is that these Iraqi forces are cut off from any kind of communication with the rest of Iraq, and are terrified they will be slaughtered.
The Iraqi division is being hammered by B52s which are wheeling about in the sky. They are taking a severe hammering, but at the moment they are hanging on.
It is likely that it is a regular Iraqi army division rather than the Republican Guard.
The Kurdish troops are working with Americans in what are being called "packets". About 120 to 150 Kurdish troops are supported by 12 to 18 Americans from the Special Forces unit.
This is essentially a Kurdish war with American air support. There are a few American ground troops, but not many.
We are pushing down towards Tikrit, but there is a limit to how far south the Kurdish peshmergas will go.
Their political masters will give them a boundary which they cannot pass - and I do not think anybody wants to upset the Americans or indeed the majority opinion in Iraq.
US forces have a limited presence on the ground
It is important for the Kurds to get on well with the other parties when the post-war constitutional talks start.
In fact, I suspect the four Kurdish soldiers who have been assigned as our bodyguards will be the only uniformed peshmergas to see Baghdad.
We now think that the town of Kirkuk has fallen to combined Kurdish and American forces. We have been receiving calls from the Kurdish command in the city telling us what has happened.
Kurdish Special Forces entered the city last night in disguise, picked up weapons, and started an uprising.
Iraqi soldiers in Kirkuk have probably taken off their uniforms and disappeared. But Kirkuk is a mainly Kurdish city and they will be terrified of the locals.
The Saddam regime has been extremely harsh with the people of Kirkuk. Over the last few weeks for instance, only one Kurd was allowed to leave a family home at a time.
So I imagine the Iraqis are feeling extremely vulnerable right now.
The capture of Mosul, we think, will be more difficult. The Kurds and Americans think it will hang on until the very end.
It is full of Arab nationalists - Sunnis who are anxious about the Kurds and Shias - and it is supported by a paramilitary force called the Jash.
The Kurds would regard the Jash as quislings who have been policing their fellow Kurds on behalf of Saddam Hussein's regime. These are men that have nothing to gain by surrender.