Rep. Gabrielle Giffords hasn't had abnormal brain swelling, and doctors at the University of Arizona Medical Center said Monday they were growing a bit more optimistic about her chance of recovery after she was shot in the head Saturday.

The congresswoman, critically wounded while appearing at a constituent session outside Tucson, remained in critical condition Monday. Hospital chief of surgery Rainer Gruessner said Ms. Giffords and seven other victims who remained hospitalized Monday "are doing better."

Twenty people were shot in the rampage, six fatally, including the chief federal district judge in Tucson, John M. Roll. Of the injured, the remaining six victims have been discharged from the hospital.

University Medical Center neurosurgeon Michael Lemole expresses optimism about Rep. Gabrielle Giffords' recovery.

While a lack of unusual swelling in the brain is a positive indicator, doctors remained cautious about Rep. Giffords' prognosis. Swelling can put pressure on brain tissue, cutting off oxygen to portions of the brain and potentially furthering the damage from the shooting itself.

A CT scan of the congresswoman showed that there has been "no progression of that swelling," said G. Michael Lemole Jr. , the hospital chief of neurosurgery and one of her physicians. "No change is good, and we have no change."

Dr. Lemole said he and colleagues were "close" to "a sigh of relief" about the congresswoman's prognosis. But he and other neurological specialists said it was still too early to know how she'll fare, including what possible deficits she might suffer in the longer term, either in her ability to think or in her personality.

"At this point, we can't measure psychological function," Dr. Lemole said at a press briefing Monday. He and other doctors at the Tucson hospital said Ms. Giffords had responded to verbal commands. These tend to be requests for a patient to wiggle toes or squeeze a doctor's hand. But, partly because she's on a ventilator and mostly sedated in a medical coma, the doctors don't yet know whether she'll recover her ability to speak or how her cognitive abilities might change.

Dr. Lemole said that the path of the bullet–which went from back left to front left of her head–may have been high enough that it missed key brain centers controlling speech, vision and cognitive function.

"The higher the trajectory, the better the hope," he said. But he and colleagues steered away from making specific predictions about her recovery.

Write to Thomas M. Burton at