Earlier reports indicated the work would take about two more months were mistaken, airport spokesman Bob Parker said Monday. The work is expected to take two months total.
There was a new participant at the scene Monday, he said.
"We brought in a crane overnight to do work," Parker said.
The tower, built about 50 years ago and upgraded in the 1970s, is 107 feet tall.
It's been closed since the 6.8-magnitude quake shook out the large windows at the tower's upper level. Air traffic controllers are working from a temporary "tower" - a specially equipped trailer perched about 80 feet high atop large shipping crates on a hillside above the runways.
The old windows were three-quarter inch glass, but are being replaced with safety glass, Parker said.
"The controllers have asked that we go with a different style glass - a laminated safety glass," he said.
When the earthquake struck, most of the tower's thick plate glass windows fell outward to the ground, and controllers were showered with ceiling tiles and other debris.
Nobody was injured and inbound flights were brought to safe landings, but Sea-Tac was closed most of the day.
Parker said the airport now is operating close to normal "during most hours of the day."
Even with the repairs, the permanent tower's days are numbered. A new 233-foot tower is under construction and should be completed in 2004.