The union for American Airlines Group Inc. pilots is redoubling its push for time in a Boeing Co. 737 Max simulator, saying aviators should be given access before the grounded plane returns to service.

Dan Carey, a veteran American pilot and head of the Allied Pilots Association, appealed to Boeing Chief Executive Officer Dennis Muilenburg a day after testifying before a Congressional subcommittee looking into two deadly crashes of the model. The APA has said that an earlier request for simulator time, which union officials made to Boeing through American, was rejected.

“Our participation in every aspect of returning the 737 Max to service and restoring public trust in the airplane is absolutely critical,” Carey said in a letter Thursday to Muilenburg. Carey asked for access to a full-motion Max simulator as soon as possible.

American is one of three U.S. carriers operating the Max, with 24 in its fleet, and Carey said more than 4,200 of the company’s pilots will eventually operate the plane once it’s approved to return to the skies. Boeing is preparing a software update designed to prevent the kind of severe, repeated dives that occurred in the two accidents after erroneous readings from a sensor. The fix is meant to lessen the need for additional pilot training.

‘We have been working closely with our pilots on the APA National Safety Committee on the suggested training and other issues concerning returning the 737 MAX back to revenue service,” Fort Worth, Texas-based American said. “We appreciate their input and collaboration.”

Boeing didn’t immediately respond to a request for comment after normal business hours Thursday.

Sully’s Call

Retired pilot Chesley “Sully” Sullenberger, who gained fame by landing a disabled jet on the Hudson River in 2009, also testified Wednesday before the U.S. House of Representatives aviation panel and called for simulator training for Max pilots.

“We should all want pilots to experience these challenging situations for the first time in a simulator, not in flight with passengers and crew on board,” he said.

Sullenberger, who has been at the controls for simulated flights with and without the Max software fix, said such training would allow pilots to physically experience the cockpit warnings and recovery procedures that crews encountered in the doomed flights. The APA has said it wants its pilots to encounter flight conditions both before and after the Boeing software update.

Only a few Max simulators have been made and no U.S. airline currently has one. Boeing provided a computer-based training course for 737 pilots transitioning to the Max, which entered commercial service two years ago. The crashes in October and March killed a total of 346 people.

Former U.S. Federal Aviation Administrator Randy Babbitt said he, too, has flown in a Boeing Max simulator since the disasters. So has a Wall Street Journal reporter who is also a pilot, and who flew one with American’s 737 fleet captain.