On this tour, the general is not scheduled to visit southern Iraq, where Shiite forces are asserting themselves more quickly than many American officials had predicted.
Most of the rival Druse and Shiite forces pulled out of positions ahead of the Syrian soldiers.
They have prevented a civil war by calling on Shiite forces to not seek revenge against Sunni terrorists.
Muhammad Bakr al-Hakim controlled the only effective Shiite paramilitary force, but had chosen not to direct it against the occupation.
And if those rival Shiite forces were to begin a fratricidal conflict, there is little the Britons would be able to do to intervene.
But even a "ruling" must be confirmed by a living senior Shiite cleric to continue in force.
In the spring, American forces won an impressive military victory against the Shiite forces of Moktada al-Sadr.
When Shiite forces took over this Sunni town, they spread out and clamped down.
But now, Shiite forces control the main roads, and American soldiers can walk freely into the central market.
These include Kurdish guerrillas in the north and Shiite forces in the south.