There seems to be no end to the Big Three automakers’ woes. This week, General Motors offered a new buyout plan to its 74,000 unionized workers in the United States — those who didn’t take the 2006 buyout offer. The Ford Motor Company and Chrysler also have plans to buy out thousands of employees. Still, there is a glimmer of hope: the companies plan to hire new workers to replace at least some, and perhaps a substantial share, of those they let go.

Foreign carmakers already have about half the American market, and analysts forecast that within the next five years they will build more cars here than Detroit’s automakers. Though the Big Three culled tens of thousands of workers in the United States in the last couple of years, they are still operating way under capacity.

Detroit’s troubles are only partly because of their failure to design cars that Americans want to buy. Labor arrangements put together decades ago, in an era of less competition, have saddled them with an older work force and higher labor costs than the Japanese and Korean companies that have set up plants in union-free states.

The American carmakers’ problems underscore the need for a government-backed system of universal health care, which would relieve some of the costs that have made competing so much harder.

The good news is that the carmakers and the union seem willing to change their old ways of doing business. As part of the new contracts, automakers agreed to put up billions in cash and other assets for trusts that would pay for retirees’ health care, taking those costs off their own books. The union allowed the companies to hire cheaper noncore workers. These measures will reduce labor costs and give Detroit a better chance to compete head to head with Toyota, Honda, Nissan and Hyundai. If Detroit’s carmakers can also design more desirable cars, this might be the beginning of their turnaround.