Giffords underwent surgery Wednesday to replace a piece of her skull that was removed Jan. 8 after Giffords was shot through the left side of her brain in an assassination attempt in Tucson, the Arizona Daily Star reported Friday.
She was well enough by Thursday afternoon to take a cellphone call from her husband Capt. Mark Kelly, commander of the space shuttle Endeavour, currently docked with the International Space Station.
Outpatient therapy is the 40-year-old congresswoman's next major medical goal and ideally it will happen during the summer, Giffords' chief of staff, Pia Carusone, said.
Though she misses Tucson, for the time being she'll remain with the medical team at TIRR Memorial Hermann rehab hospital in Houston, Carusone said.
Giffords' medical team says it has a tentative discharge date from rehabilitation for her, but said they will not disclose yet.