INCREASED OPTIMISM:

In Falluja, a town that rises abruptly out of the vast Syrian Desert an hour west of Baghdad, nearly every building left standing has some sort of hole in it.

Mosques are without their minarets. Apartment walls have been peeled away by artillery shells. A family’s kitchen is full of tiny holes made by a fragmentary grenade.

Of all the places fighting has raged since the American invasion nearly six years ago, Falluja — the site of two major battles and the town where American security contractors were killed and their bodies hung from a local bridge — stands out as one of the bloodiest and most intractable.

This month, as the last American marines prepare to leave Camp Falluja, the sprawling base a few miles outside of town where many of the American troops who fought the two battles were stationed, Falluja has come to represent something unexpected: the hope that an Iraqi town once at the heart of the insurgency can become a model for peace without the United States military.