Volkswagen AG agreed to fix or buy back about 500,000 tainted cars in the U.S., taking a significant step forward in its effort to emerge from the emissions-cheating scandal.

After months of acrimonious wrangling with U.S. authorities, the German carmaker was commended at a hearing in San Francisco on Thursday for its cooperation and given until June 21 to fine-tune the agreement. While the deal is set to cost at least $10 billion, according to a person with direct knowledge of the matter, the judge overseeing the process said specific details will remain confidential until the agreement is finalized.

“There is a definite momentum” to resolving this issue, U.S. District Court Judge Charles Breyer said at the hearing. The final deal will include “substantial compensation” for affected owners of cars rigged to cheat on official emissions tests, said the judge, who is presiding over more than 600 lawsuits linked to the scandal.

The agreement with U.S. authorities is a milestone for Volkswagen as it seeks to emerge from the seven-month-old crisis. The German carmaker has been battling to appease regulators and regain customers’ trust after admitting in September that it rigged the exhaust systems of 11 million diesel-powered cars worldwide to pass official emissions tests. The news led to the departure of Chief Executive Officer Martin Winterkorn and caused Volkswagen to delay releasing its 2015 earnings due to uncertainty over the cost of the scandal.

The stock has risen 12 percent over the past two days amid growing investor optimism over the outcome of the crisis. Volkswagen climbed 5.1 percent to 127.05 euros in Frankfurt on Thursday. The increases pared losses since the cheating became public in September to 22 percent.

Remediation Fund

The plan covers about 480,000 2.0-liter diesel vehicles in the U.S. and will include some buybacks. What to do about 85,000 VW, Audi and Porsche models with 3.0-liter engines is still to be worked out.

The accord with U.S. authorities includes a fund for remediation and has been agreed to by state and federal regulators, Volkswagen’s lawyers told the judge Thursday. Volkswagen also agreed in principle on a settlement with class-action plaintiffs, which will be finalized in the coming weeks, the Wolfsburg, Germany-based company said in a statement.

“VW is committed to winning back confidence of consumers,” Robert Giuffra, a lawyer for Volkswagen, told the court.

The deal addresses civil claims by the U.S. government and lawsuits over diesel vehicles rigged to cheat pollution controls, and Volkswagen’s legal headaches in the U.S. are still far from over. Thursday’s agreement doesn’t involve penalties or fines likely to be imposed on the carmaker. The Department of Justice said in a statement that while the agreement addresses “one important aspect” of the scandal, it’s other investigations remain “active and ongoing.”

Final Assessment

The final assessment of whether the Volkswagen agreement is a good deal for the U.S. public will have to wait until the deal is final, said Dan Becker, director of the Washington-based Safe Climate Campaign.

“The devil is in the details, and there aren’t a lot of details,” Becker said.

The German carmaker, which has so far set aside 6.7 billion euros ($7.6 billion) for the recalls, is set to discuss further financial impacts from the scandal at a supervisory board meeting on Friday. Sales have also struggled, with Volkswagen’s first-quarter market share reaching a five-year low in Europe.

Volkswagen’s struggle to come to terms with U.S. authorities contrasts with a relatively easy process in Europe, where about 8.5 million vehicles are affected. Less stringent regulation helped VW get initial approval in December for a low-cost fix in its home region that consists mainly of software updates and in some cases a tube that regulates air flow. There’s been no offer to compensate European customers.

The case is In Re: Volkswagen “Clean Diesel” Marketing, Sales Practices and Products Liability Litigation, MDL 2672, U.S. District Court, Northern District of California (San Francisco).