Ron Barber, Giffords' district director, left the hospital this morning and will attend the funeral of Federal Judge John Roll, who was killed in the attack, later today.
Giffords, doctors say, continues to make strides.
Doctor Pete Rhee, head of the University Medical Center trauma unit, says Giffords is opening her eyes more frequently and is performing more complex brain tasks -- sometimes on her own, without prompting from doctors.
Doctors have not yet removed Giffords' breathing tube, which, they say, will be the next milestone in her recovery.
The tube could possibly be removed as early a today.