The security improvements in most neighborhoods are real. Days now pass without a car bomb, after a high of 44 in the city in February. The number of bodies appearing on Baghdad’s streets has plummeted to about 5 a day, from as many as 35 eight months ago, and suicide bombings across Iraq fell to 16 in October, half the number of last summer and down sharply from a recent peak of 59 in March, the American military says. As a result, for the first time in nearly two years, people are moving with freedom around much of this city. In more than 50 interviews across Baghdad, it became clear that while there were still no-go zones, more Iraqis now drive between Sunni and Shiite areas for work, shopping or school, a few even after dark. In the most stable neighborhoods of Baghdad, some secular women are also dressing as they wish. Wedding bands are playing in public again, and at a handful of once shuttered liquor stores customers now line up outside in a collective rebuke to religious vigilantes from the Shiite Mahdi Army. Iraqis are clearly surprised and relieved to see commerce and movement finally increase, five months after an extra 30,000 American troops arrived in the country. But the depth and sustainability of the changes remain open to question.