Doctors have removed bone fragments from U.S. Rep. Gabrielle Giffords' fractured eye socket.

The fragments were removed this weekend to relieve pressure, her neurosurgeon at University Medical Center, Dr. Michael Lemole, said at a news conference today. Doctors removed the bone chips and reconstructed the roof of the eye socket through an incision above her eyebrow, he said.

Giffords also had surgery over the weekend to replace her breathing tube with a tracheotomy in her windpipe. Her condition was upgraded from critical to serious.

Giffords, 40, was shot though the skull on Jan. 8 outside a Tucson, Ariz., supermarket where she was meeting with constituents. She can respond to simple commands and move her limbs, but can't talk because of the breathing tube. Doctors say it's too soon to know if she'll suffer cognitive problems.

"I'm happy to say that within a few hours of the surgery, she was waking up, and through the weekend she came back to the same baseline she had been before the surgery -- that same level of interaction she's having been having with us," Lemole said. "That's all very good."

He added, "At this time, we're hoping to continue tying up those loose ends and get her ready for that third phase of her care, the rehabilitation."

A gunman shot Giffords and 18 others. Six people were killed, and 13 were wounded. Giffords and two others remain hospitalized. A suspect, Jared Loughner, is being held in a prison outside Phoenix on murder charges.