NEW YORK (CNN/Money) - American Airlines apparently dodged the threat of bankruptcy Friday for the fourth time in the past month when its flight attendants union agreed to a concession contract with the airline.

A split board of directors of the Association of Professional Flight Attendants gave final approval to its concession pact, saving deals for $1.6 billion in labor cost reductions annually from itself and two other major unions. The savings come from across-the-board wage cuts for union members and changes in work rules that will allow additional staffing cuts, and allow the world's largest airline to stay out of bankruptcy court.

The unions' final approval with American Airlines parent AMR Corp. came after the company gave in to some union demands for changes in the agreements, and after CEO Don Carty resigned Thursday evening due to controversy over executive compensation.

Shares of AMR (AMR: up $0.36 to $4.40, Research, Estimates) were up about 20 percent following news of the flight attendants deal.

American, which also imposed about $200 million in annual labor cost savings on its nonunion employees, said it needed $1.8 billion in savings in order to stay out of bankruptcy. The airline came to the brink of bankruptcy three times since March 31, and was prepared again to go to bankruptcy court in New York as early as Friday if it didn't get the necessary union approvals.

American Airlines executives praised the unions for finally signing off on the concession pacts after a tumultuous week, but they also warned that the airline's financial problems are not behind it.

"I commend you in taking this step to move the company forward," Gerard Arpey, who was named AMR's new CEO Thursday evening, told a gathering of employees at AMR headquarters in Fort Worth, Texas Friday afternoon. "I recognize these new contracts involve enormous sacrifices by our employees. We have our work cut out for us; we are not out of the woods yet."

Employment deals for Arpey and Brennan and Carty's severance deal had not been finalized by Friday afternoon, according to AMR spokesperson Bruce Hicks.

The APFA along with the Allied Pilots Association and Transport Workers Union, which represents American's ground workers, all ratified the six-year concession contracts last week. But revelations about compensation packages for American's top executives prompted union outcry and threats to withhold final approval of the deals.

CNNfn's Greg Clarkin reports from Fort Worth, Texas, on the concession agreement between AMR unions and management. Play video (QuickTime, Real or Windows Media)

American pulled back part of the controversial compensation plans April 18 when it rescinded retention bonuses for the company's seven highest-ranking officers. It did not drop contributions it had made to a trust fund to protect pension payments for its 45 top-paid executives, though.

Carty, 56, apologized to the unions and the other employees Monday, admitting he made a mistake in not informing the unions of the compensation packages before their members voted on the concessions. He said Thursday he was resigning because "my continuing on as chairman and CEO of American Airlines is still a barrier that, if removed, could give improved relations -- and thus long-term success -- the best possible chance."

Arpey, 44, who had been Carty's No. 2, serving as president and chief operating officer since last year, said that restoring trust with American employees would be a top priority.

"It will come as no surprise to anyone there is a definite need to rebuild trust at our company," he said.

Former AMR CEO Don Carty.

He apparently has the trust of Allied President John Darrah, who told the gathering at American's headquarter that there is no one in the world he has more trust and respect in. He also praised Carty, saying that the former CEO "was not in this for self interest. It was the airline first and foremost."

Flight attendants union President John Ward also thanked Carty and Arpey for doing everything they could to keep the airline out of bankruptcy. But Ward was a bit more cautious in his endorsement of the new management team than the pilots union president, telling the same gathering, "We will not travel down this path in the blind faith everything will get better.

The AMR board also named director Edward Brennan as "executive chairman" of the board. An AMR director since 1977, Brennan is the retired chairman and CEO of Sears Roebuck & Co.

One key to winning union agreement for the contracts after the outcry erupted was a 12-hour meeting between management and union leadership Wednesday. There, management agreed to a union demand to shorten the contracts to five years rather than six, and agreed to some additional contract enhancements.

Those change helped win over the pilots and TWU, which gave final approval their contracts Thursday. But the flight attendants held out their approval until midday Friday.

New leadership team at AMR - CEO Gerard Arpey, left, and Executive Chairman Edward Brennan.

The APFA Web site said the union's executive board split 13-5 to approve the deal. The resolution approved by the board said the shorter length of the deal, Carty's resignation, and the threat of deeper pay and staffing cuts for the flight attendants were the reasons for it voting "with great reluctance" to give final OK to the labor contract.

One airline analyst said he believes Carty's departure was unfortunate but probably unavoidable, given the controversy over the executive compensation packages.

"The cover-up is usually worse than the sin. The union leaders were embarrassed and understandably so," Ray Neidl, airline analyst with Blaylock & Partners, said on CNNfn's Market Call Friday morning. "Don was a sacrificial lamb. He made a mistake and he's paying the price. It's unfortunate because American is losing a really seasoned executive."

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Airline management had said that in case of a bankruptcy filing the lenders that would be funding operations during reorganization would have demanded $500 million in additional cost savings on top of the $1.8 billion in cuts agreed to or imposed.

American Airlines posted a $1.05 billion loss Wednesday that was nearly twice as large as the year-earlier loss and larger than forecast by analysts. Even though its traffic and revenue stayed roughly even with last year, rising fuel prices resulted in a situation Carty described as "truly dreadful."

Still, the wage cuts, which are effective May 1, will help dramatically reduce losses. Neidl said he believes the final union agreement reduced the chance of a bankruptcy at AMR to about 20 percent.