At least four more bodies were recovered on Sunday, bringing the count to 34. The remains were transferred by helicopter to the processing center in Pangkalan Bun, Indonesia, to the north of the search area.
The developments came as Indonesian officials announced that they had identified three more bodies -- two female passengers and a male flight attendant.
Additional wreckage was spotted overnight, measuring almost 10 meters (33 feet) by 1 meter.
Sunday's progress was not as great as searchers had hoped. It was forecast to be the best day weather-wise for the search, but choppy seas once again hindered the operation.
Initial compensation offered
As many endured the agonizing wait for news of their loved ones, CNN obtained details of initial compensation packages from AirAsia to the families of the victims.
Several family members told CNN on Sunday that families of those on board the plane were presented with a draft letter from AirAsia outlining details of preliminary compensation.
The letter states that families are entitled to about $24,000 for each family member who was on the plane.
While some families signed the letter, others requested revisions to the wording.
This compensation money is for any "financial hardships" during this period of the search, and in the letters AirAsia stressed that it was not a confirmation that their family members were deceased.
Taking advantage of better weather, the surface search area has been extended to the east, Marsdya Bambang Sulistyo, head of the Indonesian Search and Rescue agency, told reporters Sunday.
Although there has been an improvement in conditions, they remain difficult, with heavy rain and high waves continuing to hamper recovery efforts.
The surface search's extension was based on predictions that the remains of the victims, along with wreckage from the aircraft, have drifted with the current.
The priority surface and underwater search areas remained the same, he added.
Twenty aircraft and 27 ships were involved in Sunday's search. Divers are on standby but the underwater search was halted due to poor visibility and strong currents.
Three more bodies -- still wearing seat belts -- were spotted on Friday, an Indonesian marine corps major, Professor De Greatsman, said.
Search teams have found several large pieces of debris believed to be parts of the aircraft. Sulistyo said the latest objects -- including one that is 18 meters long -- were located by sonar in the priority search area.
Searchers came upon the metal parts after spotting an oil slick late Friday.
Anton Castilani, head of the Disaster Victims Identification unit, is eager to get the rest of the victims out of the water before they sink to the bottom of the sea. He is in charge of identifying them and said that gases in the bodies that keep them afloat disperse after a few days in the water.
He urged families to be patient with his team as they identify loved ones. He wants to do his work right. "We have to make sure that we have to return that right body to the right family," he said.
Decomposition also slows his work down. "The later the dead bodies come to you, the harder you work," he said. His team uses fingerprints and dental records as well as DNA to find out who they have recovered.
On Friday, the USS Sampson, which the U.S. Navy has deployed to help, recovered some bodies.
A limited number of them will be autopsied to determine the cause of death to aid the investigation, an Indonesian official said Saturday. But many families don't want autopsies done.
"For the sake of the investigation, we agree, and it is accepted by Interpol, to perform autopsies on the pilot, co-pilot and some randomly selected passengers," said East Java Police Chief Anas Yusuf.
Nine of the plane's victims have been identified with the addition of the three victims' names on Sunday.
Finding the fuselage and flight data recorders of the Airbus A320-200
has priority for the 59 diving teams searching underneath the waves. Russia has joined the effort with 22 underwater teams along with a search plane and a cargo jet.
The searchers are concentrating on a 1,575-square-nautical-mile zone that officials believe is the most probable area to find the remains of the aircraft.
Here's where things stand on Flight QZ8501:
What we know: QZ8501 took off early December 28 from Surabaya, bound for Singapore. Roughly 35 minutes into the flight, the pilot asked air traffic control for permission to turn left and climb to avoid bad weather. Minutes later, the plane disappeared from air traffic control's radar.
What we don't know: What happened on board after contact with the plane was lost. No distress call was received.
Some experts speculate that the aircraft experienced an aerodynamic stall because of a lack of speed or from flying at too sharp an angle to get enough lift. Other theories include a lack of information about the plane's position or storm damage to the engines.
What we know: The "black boxes" are key. Actually, the flight data recorders are orange and should be in the plane's tail. A lab in Jakarta will analyze them, if they are recovered. The batteries powering the "pingers" that send acoustic signals have only about three weeks of power left.
What we don't know: What destroyed the plane. Investigators will need to use information gleaned from the flight recorders and clues from the wreckage to try to find out.
"The more bits I can put into my mosaic, the better my picture will be," aviation safety expert Michael Barr said.
The plane and the pilots
What we know: The Airbus, operated by AirAsia's Indonesian affiliate, had accumulated about 23,000 flight hours in about 13,600 flights in six years. The plane's last scheduled maintenance was November 16.
Flight 8501's veteran captain, Iriyanto, 53, had 20,537 flying hours, 6,100 of them with AirAsia on the Airbus A320, the airline said. The first officer, Remi Emmanuel Plesel, 46, had 2,275 flying hours, a reasonable amount for his position.
Indonesian authorities are looking into why AirAsia was flying that particular route on that particular day, a Sunday; the country's Transport Ministry says that AirAsia was permitted to fly it only on Mondays, Tuesdays, Thursdays and Saturdays. AirAsia said it will cooperate with the inquiry and suspended all service from Surabaya to Singapore in the meantime.
What we don't know: Did technical problems or human error have anything to do with the crash? A major aviation database registers 54 incidents involving the A320.
Some A320 accidents and incidents involve fan-cowl detachments, landing gear collapse, bird strikes and pilot error, an expert said. These cause disasters only in very rare cases.
Meanwhile, the U.S. Embassy in Jakarta issued a security alert Saturday
after being "made aware of a potential threat against U.S.-associated hotels and banks in Surabaya." A State Department official, however, told CNN that there was "no knowledge of any connection between this threat and the AirAsia flight."
No additional information was given regarding the nature of the threat, but the embassy recommended "heightened vigilance and awareness of one's surroundings when visiting such facilities."