(CNN) -- U.S. Rep. Gabrielle Giffords is "recovering well" after skull surgery Wednesday, officials at Memorial Hermann-Texas Medical Center in Houston said.

The Arizona Democrat had a cranioplasty procedure, officials said.

Doctors will discuss the procedure and Giffords' next step in rehabilitation at a Thursday morning press briefing.

Jared Lee Loughner is accused of opening fire outside a Tucson, Arizona, supermarket where Giffords was meeting with constituents in January. Six people -- including a federal judge -- were killed and 13 others were wounded in the attack.

After the shooting, surgeons in Arizona cut a hole in Giffords' skull to give her brain space to temporarily swell. The congresswoman later was transported to Houston for further treatment and rehab.

Dr. Dong Kim told CNN's Elizabeth Cohen before the surgery he would implant a piece of synthetic bone made specially for the congresswoman.

"More than just getting the bone back, it is a marker for where we are" in Giffords' recovery, the neurosurgeon said.

Kim told Cohen that a shunt may have to be inserted to carry excess fluids from the brain to the abdominal cavity.