Giffords uses her left side and has begun making limited use of her right arm and leg, a common effect of a bullet wound on the left side of the brain, said Dr. Gerard Francisco, chief medical officer at Houston's TIRR Memorial Hermann who works with Giffords daily.
"Her left side is perfect," said Pia Carusone, her legislative chief of staff. "She can do whatever you can do."
Nurse Kristy Poteet said Giffords pushes a cart up and down the hospital halls as therapy, focusing on using the correct muscles. More therapy comes from games of bowling and indoor golf.
The Republic report - containing interviews over the past few days with her husband, doctors and others close to her - gives the latest picture of her recovery 15 weeks after a gunman opened fire in a Tucson parking lot, killing six people and wounding 13 others, including Giffords.
The physicians place her in the top 5 percent of patients recovering from her type of brain injury, the newspaper said.
"She shows a lot more independence right now," Francisco said. "She's her own person."
Giffords' husband, Mark Kelly, said in an interview with CBS News that she'll attend Friday's launch of his space shuttle mission in Florida. It will be the first time Giffords has traveled since she was flown from Tucson to Houston more than three months ago to undergo rehabilitation for the gunshot wound to her head.
"I've met with her doctors, her neurosurgeon and her doctors, and ... they've given us permission to take her down to the launch," said Kelly, who is commanding the shuttle mission.
CBS released excerpts of the interview Sunday, and it was scheduled to air Monday on "CBS Evening News with Katie Couric."
Kelly told the Republic that Giffords longs to leave the rehab center for good, repeating "I miss Tucson." When that day comes, Giffords told Poteet she plans to "walk a mountain."
Dr. Dong Kim, the neurosurgeon who oversees Giffords' care, said most of the physical and speech recovery happens within 12 months.
Those closest to Giffords tell of a woman progressing from severe brain trauma, but their words are without heightened expectations.
She speaks most often in a single word or declarative phrase: "love you," ''awesome," those close to her said.
There were hopeful language signs even in March when Kelly said Giffords learned about the people killed during the Tucson rampage Jan. 8.
Kelly said he was reading a newspaper story about her out loud when she noticed he skipped a paragraph. That paragraph told of the casualties in the Tucson shooting - news that set Giffords grieving.
"So many people, so many people," Giffords repeated. Poteet said she would find Giffords with heavy looks on her face, repeating "no-no-no-no-no."
For that reason, Kelly said he hasn't told her that the victims included her friends and colleagues Gabe Zimmerman and Judge John Roll, or a 9-year-old girl, and three others, the kind of older constituents she loves to help.
Kelly said he wants her to be able to process the emotions without fighting so hard for the words.
"The challenge is she knows what she wants to say, and she knows everything that's going on around her," Carusone said, but can't always express it.
The Republic reported that Kelly comes in the morning with coffee and the newspaper, heads to work at NASA, and returns to Giffords at night to talk. Sometimes, he takes a nap with his wife in her hospital bed, holding her close.
When he comes into the room, Giffords breaks into an oversized smile, Poteet said, reaching out her good arm to beckon him to her side, give him a half-hug.
Kelly, who has been to space before, said his job "will be a little bit harder this time, just because I want to look out for her."
He intends to phone Giffords during the mission, but he expects the conversations will be different than on his last flight.
Now, he will ask her "how things are going and how she's doing and what's her day like," he said.
They have a particular phone goodbye, "but that's a secret," he said.