Flight cancellation numbers were finally trending down Saturday for the first time in a week, suggesting a slow recovery from Harvey’s effect on aviation may finally be under way.

More than 600 flights have been grounded on Saturday and preemptive cancellations already stretched into next week, according to flight-tracking service FlightAware.

But Saturday’s tally marked a significant improvement from the Harvey-related woes of the past week, when more than 1,100 flights were canceled each day since last Saturday (Aug. 26). About 400 flights had already been canceled for Sunday and another 175 for Monday.

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Nationwide, more than 12,000 flights have been canceled since Harvey first began affecting flights in Texas. Nearly all of those have come in Houston, where the city’s Bush Intercontinental and Hobby airports have been the hardest hit by the storm.

Both airports had closed by Sunday and remained so through Wednesday afternoon. Even then, their restart has been slow.

Southwest, for example, wasn’t expected to begin flying at all at Hobby airport until noon local time on Saturday. Southwest is by far the busiest airline there.

United has been ramping up its schedule at Bush Intercontinental, where the carrier operates its second-busiest hub. But even United has warned it could take weeks until its Houston operations are completely back to normal.

The agency that runs the two Houston airports advised fliers to expect continued disruptions, and not to come to the airports unless they had confirmed the status of their flights.

“The plan is to begin a phased return to service, with full service expected by the end of Labor Day weekend,” Houston Airports said in a Friday statement. “Contact your air carrier for specific flight status updates regarding your flight. Only those with a ticket for a confirmed scheduled flight should come to the airport. Many roads around the City of Houston are still unsafe for travel, therefore, we urge all passengers to take their time arriving to the airports and to solidify a safe route to and/or from our facilities.”

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