Doctors put a plastic implant in place to fully cover her brain. It replaces a piece of skull that was removed to relieve swelling from a gunshot wound.
The surgery is another milestone in Giffords' recovery from an assassination attempt back in January.
Doctors will now be focusing on the next stages of her rehabilitation. The successful surgery is a big relief for Giffords' husband, Mark Kelly, who is commanding the shuttle Endeavour crew on the /*International Space Station*/.
Kelly said he kept in touch with family and friends throughout the surgery and is pleased with how it went.
"This has been a long road since Jan. 8 for us. Her having surgery yesterday was not planned all along, but she was ready and the doctors wanted to do it then and it didn't make sense to wait until I got back," said Kelly.
Meantime, Kelly's crew has accomplished the No. 1 objective of their mission.
They've attached a cosmic ray detector to the International Space Station, which will study the invisible universe, searching for both antimatter and dark matter.
