After days in which her city was convulsed with war, bombing, looting and arson, Tadamoun Abdel-Aziz went shopping for the first time in more than a week, buying a package of 30 eggs, some bread and vegetables.

With looting and mayhem subsiding, the Iraqi capital and other major cities are slowly returning to normal, as evidenced by this veiled Baghdad woman, who ventured outside Tuesday to find once-shuttered stores reopened.

"The market is open and products are available," she said as she walked with her son, who carried a bag filled with bread.

Many stores closed after the war started on March 20, and with the collapse of Saddam Hussein's regime on April 9 — and the ensuing chaos — most stayed shuttered. Some were set on fire by looters.

On Tuesday, however, scores of people roamed the downtown Irkheita Market to buy meat, vegetables and fruit, while others sat in cheap restaurants eating grilled meat or drank tea in coffee shops.

Nevertheless, many grocers said their shelves remained half-empty because the Shorja market, their main supplier and Baghdad's largest market, was still closed.

"I am selling some vegetables and some of the stuff that remains in my shop," said grocer Issam Saleh, 38. "Shorja has not opened yet, but God willing things will improve."

And electricity, water and phone service have yet to be fully restored. With the temperature in the 90s, people bought 3-foot blocks of ice for about $1.15 to make cold drinks.

"My coffee shop is still closed because there is no gas, electricity or water. People are coming to the restaurant to eat because meat is grilled on charcoal," said Khalil Mohammed, 69.

It could take weeks to fully restore Iraq's power grid and water system, though some cities are already showing good progress, said U.S. Army Lt. Col. Kevin Kille, operations officer at the coalition's Humanitarian Operations Center in Kuwait.

Access to water and electricity is generally better in cities that were the first to fall, such as Umm Qasr and Karbala, and worse in those taken later, like the northern cities of Mosul and Kirkuk.

Initially, power was restored in Iraq's cities through portable generators, and water was brought in by aid workers. But the focus has now turned to repairing the infrastructure so towns are self-sufficient. Often, fixing the power restores running water because the water pumps run on electricity.

About 40 percent of Baghdad is now getting power at least part of the day, Kille said.

"The basic necessities of food and water and power, it's coming in," he said, "and I think the people are satisfied that relief is already in place and that more is coming."

In Baghdad on Tuesday, cars jammed the usually busy streets of the Rasafah neighborhood on the east bank of the Tigris River.

"We are seeing more police and American patrols in the streets, and people are going out more now. This shows that the situation will be better," said Zuheir Saleh Ahmed, eating lamb kabob at a restaurant.