By Paul Rincon
BBC News science reporter, Houston
Nasa is considering whether to send an astronaut out on a spacewalk to make repairs on the underside of the space shuttle Discovery.
The first spacewalk lasted about seven hours
They are currently looking at the best option for getting a crew member to the underside of the vehicle safely to trim two protruding gap fillers.
Gap fillers plug the spaces between shuttle heatshield tiles, which are made of ceramic fabric.
Shuttle managers hope to come to a decision on Monday.
One option would be for the astronaut to be ferried to Discovery's belly by the International Space Station's robotic arm.
"We have a team of folks working aggressively to go and make that gap filler safe if we decide it's an issue. We have a separate team looking at the effects of leaving that gap filler protruding," mission flight director Paul Hill said.
They are also deliberating over which is the better option to repair the gap fillers.
"We have various options from pulling the gap filler out to trimming it back to pushing it back into the gap," Mr Hill said.
Experts are confident the shuttle will return safely to Earth
The concern is that any material dangling from the shuttle during re-entry could overheat and subject tiles downstream of it to increased heating.
Different parts of the shuttle's underside are designed to withstand different levels of heating.
So experts will have to determine if the shuttle can cope with these increased temperatures during the return to Earth.
But it is especially a concern if tiles downstream of the gap fillers are nicked or chipped.
Mr Hill said a spacewalk to repair the gap filler could be done on the one-day extension shuttle managers have given the mission, but that this was "a very low likelihood".
He said it was more likely that if gap fillers were to be repaired, it would be carried out on the third planned spacewalk of the mission.
Two-and-a-half years ago, a suitcase-sized piece of foam fell away from space shuttle Columbia during its launch and punched a hole through heatshield panels in the left wing.
The damage did not present problems in orbit, but as the vehicle tried to re-enter Earth's atmosphere on 1 February 2003, super-heated gases entered the wing and tore the ship apart.
Nasa has spent years trying to make the shuttle safe to fly again.
Astronauts aboard the shuttle-space-station complex spent most of Sunday unloading tonnes of supplies from the visiting ship and transferring them to the International Space Station.
They are now also transferring computers, office supplies, food, water and other items from Discovery.
The US space agency has extended Discovery's mission by a day to allow time to unload the extra cargo, with the shuttle's return to Earth now set for 8 August.
The transfer has been given added urgency by Nasa's decision to ground the shuttle fleet after this mission.
"Once we got news of the debris coming up the tank and we'd also had some pictures turned up that showed it to us, we were of a single mind up here, I think; that it was necessary to stop flying in order to repair this problem," Discovery crew member Andy Thomas told Fox News on Sunday.
On Saturday, shuttle managers announced that following a damage assessment of heatshield tiles and thermal blankets, they had been cleared for the journey back to Earth.
They said they expected the reinforced carbon-carbon panel part of Discovery's heatshield to be given a clean bill of health on Monday.
"We looked at the photography, and from what we have seen, there appears to be very little damage in the tiles," Discovery crew member Charles Camarda told Fox News.
"It looks like it's a clean vehicle, and we're good to go to return home."
Nasa also released stunning footage from cameras mounted on the shuttle's solid rocket boosters as they climbed to orbit and were jettisoned, showing their fall through the atmosphere to a splashdown in the ocean.