The Federal Aviation Administration did announce Wednesday night that airlines won’t have to cut more than 6% of flights at those airports because air traffic controller staffing has improved significantly in the last few days. Originally the order that took effect last Friday called for those flight cuts to increase to 8% Thursday and top out at 10% on Friday.

A number of air traffic controllers missed work while they were going without pay during the shutdown, and the spike in understaffing at airport towers and regional control centers prompted the flight cut order due to concerns about safety. The existing shortage of several thousand controllers is so bad that even a small number of absences in some locations caused problems.

Officials at FAA and the Transportation Department didn’t offer any updates Thursday morning about when they will decide to lift the order. Transportation Secretary Sean Duffy has said the decision will be based on the safety data that experts at the FAA are watching closely.

The airlines say they will be ready and expect that normal operations will resume within three or four days after the order is lifted. Some experts have suggested that problems might linger longer than that and could affect Thanksgiving travel, so it is difficult to predict whether the airlines will be able to recover from this as quickly as they do after a major snowstorm disrupts their operations and leaves planes and crews out of position.

The airlines focused their cuts on smaller regional routes to minimize the impact on their main hubs. By late Thursday morning, about 1,000 flights had been cancelled across the country.

“We are eager to resume normal operations over the next few days once the FAA gives clearance. We look forward to welcoming 31 million passengers—a new record—to our flights during the upcoming Thanksgiving travel period, beginning next Friday,” the Airlines for America trade group said Thursday.

Duffy has said that controllers and other FAA employees should receive 70% of their back pay within 24-48 hours of the end of the shutdown with the rest to come over the next couple paychecks. The financial pressure on controllers drove some of them to seek out side jobs to help make ends meet and call out of work while they dealt with the stress.

Last Saturday, the staff shortages peaked when 81 different FAA facilities warned they were running low on workers, forcing the airlines to cut additional flights. On Thursday morning, the FAA didn’t list any staffing warnings at airports and other radar facilities across the country.

American Airlines CEO Robert Isom and Chief Operating Officer David Seymour told employees in a letter Thursday that they are already seeing improvements as controller staffing stabilized over the last day or so even though more flight cuts will be needed until FAA lifts the order. But travelers should already be seeing fewer delays and cancellations on the day of their flights.

The two executives said they believe American Airlines’ planning and efforts to minimize disruptions will help the carrier bounce back fast and “deliver a strong Thanksgiving operation,” noting that millions of travelers “deserve the certainty.”