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Though New Orleans was spared the devastating damage many feared Hurricane Gustav could unleash, the Louisiana governor warned Tuesday that the state had still sustained a significant hit.

Gov. Bobby Jindal told reporters that the most serious threats remained strong downpours and the possibility of tornados.

"The greatest dangers are heavy rains," Jindal said. "Many of us are relieved ... We didn't have widespread flooding. But this is still a very, very serious storm that has caused major, major damage in our state."

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He said there have been unconfirmed reports that parts of northern Louisiana had been badly battered, and there was a lot of work still to be done.

Gustav was downgraded to a tropical depression early Tuesday.

Anxious evacuees who were scattered across the country clamored to come home to the Big Easy Tuesday, but New Orleans Mayor Ray Nagin warned they may have to wait in shelters and motels a few days longer.

The city's improved levee system helped avert a disaster like Hurricane Katrina, which flooded most of the city, and officials got an assist from a disorganized and weakened Gustav, which came ashore about 72 miles southwest of the city Monday morning.

Eight deaths were attributed to the storm in the U.S. after it killed at least 94 people across the Caribbean.

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But New Orleans was still a city that took a glancing blow from a hurricane: A mandatory evacuation order and curfew remained in effect.

Electric crews started work on restoring power to the nearly 80,000 homes in New Orleans — and more than 1 million in the region — that remained without power after the storm damaged transmission lines that snapped like rubber bands in the wind and knocked 35 substations out of service.

"We have a massive caravan of crews coming to the city and they should be here this morning to fix the rest of the power outages," Nagin said on CBS "Early Show."

The city's sewer system was damaged, and hospitals were working with skeleton crews on backup power. Drinking water continued to flow in the city and the pumps that keep it dry never shut down — two critical service failings that contributed to Katrina's toll. The FAA said the city's airport was expected to reopen at 7 p.m.

Mandatory evacuation orders were lifted for three Southeast Texas counties.

The storm's maximum sustained winds decreased to near 35 mph as it puttered toward northern Louisiana and east Texas. Up to 8 inches of rain was expected and flood warnings were posted.

Nagin cautioned that Tuesday would be too early for residents to return to New Orleans, but their homecoming was "only days away, not weeks." He apologized to the Republicans, which put the pagentry of their convention on hold to wait for Gustav to move through the Gulf Coast.

"You know, I think Gustav rained on their parade, on their little party," said Nagin, a Democrat, who cut his own trip short to his party's convention to prepare for the storm. "And hopefully they can rekindle. We'd love to host them in New Orleans next week, and they can come down and we can show them how to really do it right."

Crews would comb the city Tuesday to fully review the damage, Nagin said, with the goal of having residents return beginning late Wednesday or Thursday.

Retailers and other major companies could start sending workers Wednesday to check on their locations, he said. Buses are in place and ready to bring residents back with instructions to drop them off as close as possible to their homes.

Oil companies and rig owners, which shut down virtually all oil and natural gas production in the Gulf as Gustav approached, headed out to look for damage. Some were already putting equipment and people back in place to resume operations, and a $8 drop in the price of a barrel suggests traders are confident the storm didn't cause much damage.

President Bush, monitoring the storm from Texas said Tuesday that while it's too early to assess Hurricane Gustav's damage to U.S. oil infrastructure off the Gulf Coast, it should prompt Congress to OK more domestic oil production. He said when Congress comes back from recess, lawmakers "need to understand" that the nation needs more, not less domestic energy production.

The state and city took pride in a massive evacuation effort that succeeded in urging people to leave or catch buses and trains out: Almost 2 million people left coastal Louisiana, and only about 10,000 people rode out the storm in New Orleans.

"I would not do a thing differently," Nagin said. "I'd probably call Gustav, instead of the mother of all storms, maybe the mother-in-law or the ugly sister of all storms."

But thousands of people were strained by sleeping in cots in gymnasiums and convention centers, far away from their homes and wondering when they could go back. Fights broke out at an overcrowded shelter in Shreveport. Doctors worried about medications running out and seven people were hospitalized, all in stable condition.

"People are desperate. They don't know if they are going to have a place to go home to," said Emma McClure, 37, who was at the shelter with her three children, three sisters and some 20 nephews. "They had three years to plan this and now I wish I had stayed in the city like I did during Katrina."

Though the big city was spared, Gustav devastated parts of Cajun country, destroying homes and flooding parts of the mostly rural, low-lying parishes across the state's southeastern and central coast that are also home to the state's oil and natural gas industries.

Four evacuating Louisianans were killed in Georgia when their car struck a tree. A 27-year-old Lafayette man was killed when a tree fell on his house as the storm whipped through, and an Abbeville couple was killed when a tree fell on a home in Baton Rouge. A woman from Jefferson was killed Monday when her vehicle ran off Interstate 10 and struck a tree.

Roofs were torn from homes, trees toppled and roads flooded. A ferry sank. Telephone service was spotty at best. Parts of the Mississippi Gulf Coast were isolated by flood waters, and Gov. Haley Barbour urged residents not to return to their homes until Wednesday.

More than 50 patients had to be evacuated overnight from two small community hospitals in central Louisiana after the storm knocked out their generators, according to Richard Zuschlag, chief executive of Acadian Ambulance. The patients were taken to two Lafayette hospitals.

State officials were working with most of the 72 hospitals that had to find other shelter for patients in what Jindal described as the "largest medical evacuation in our nation's history."

Contact has been made with about 52 of those facilities; the other 20 that authorities were still trying to check up on are smaller hospitals believed to have been completely evacuated.

Jindal said he heard reports of widespread damage across Terrebonne, Lafourche and St. Mary parishes. Crews were expected to fan out and in search of injured or killed people with helicopter crews.

To the east of the city, Jindal said state officials were planning an aerial tour on Tuesday to gauge damage to Port Fourchon, a vital energy industry hub where huge amounts of oil and gas are piped inland to refineries.

Two houses built up on pilings to avoid flooding were not spared by the wind that tore through Montegut, a small Terrebonne Parish town south of Houma.

Across a narrow bayou running past the houses, globs of yellow insulation had collected in a tree and a neighbor's chain-link fence.

One of the homes had part of a wall ripped away, exposing a room with two plaques on the wall, one of which read: "Ashley Pennison, 2000-2001 honor graduate, 3.5 GPA."

The remnants of her childhood lay scattered about the soggy grass, including strung-together letter-shaped pillows spelling out her first name along with an assortment of miniature clowns.

Danny Price, the owner of a grocery store across the street, said he stayed home for the storm, but he might not the next time.

"I got scared," he said. "It was bad when the wind started rolling in. This was a picture to see: trees snapping off, fences blowing down and that wind just coming down the driveway over 100 miles per hour. It gets you scared. It's not something to play with. I don't think I'm going to stay for another one."

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The Associated Press contributed to this report.