Shot US politician recovers after op.
There were no complications from the surgery, and Ms Giffords is improving so much that she was able to give her husband a back rub. Dr Randall Friese said Mark Kelly, an astronaut, had also told doctors he saw Ms Giffords smile.
The doctor said sometimes people see what they want to see, but that "if he says she's smiling, I buy it".
Ms Giffords still cannot speak because of a tracheotomy done so the breathing tube could be removed from her mouth. Dr Michael Lemole said the eye operation entailed making an incision above the eyebrow, removing bone chips to relieve pressure and reconstructing the roof of the socket.
Ms Giffords responded from the moment she arrived at the emergency room on January after being shot point blank in the head on January 8 outside a store in Tucson, Arizona.
At first she squeezed a doctor's hand, then she raised two fingers. She opened her unbandaged eye shortly after President Barack Obama's bedside visit last Wednesday.
Then, more milestones - which doctors said were all indicative of higher cognitive function - were achieved, all with her husband at her side.
Mr Kelly asked her to give him a thumbs-up if she could hear him. She did more than that. She slowly raised her left arm. By the end of the week, she had moved her legs and arms.
At the hospital, more than 100 people were gathered amid the sea of get-well balloons and cards when the University of Arizona put out a statement upgrading her condition.
Doctors decided to upgrade her condition because the tracheotomy done a day earlier was uneventful, hospital spokeswoman Katie Riley said.
A feeding tube was also put in on Saturday, and doctors speculated that they might soon know if she could speak.
Few people survive a bullet to the brain - just 10% - and some who do end up in a vegetative state.