So far this month 35 American soldiers have been killed in Iraq. American officers arrested twenty people suspected of links to al-Qaeda.
But precisely who the enemy are - former members of the regime, ordinary Iraqis resisting the occupation and foreign jihadis - remains for them a worryingly closed book.
Our Diplomatic Editor Mark Urban travelled to the Iraqi capital Baghdad, as well as the southern city of Basra, home to British forces.
But he began his report in Falluja, where American forces face continuing resistance deep in the heart of the so-called Sunni triangle.