Although the price tag for a government bailout of the auto industry has increased, the changes the car companies are willing to make to get the federal help are moves in the right direction. In appealing for a second time to Congress for money, the country’s three automakers pledged to reduce their work force and dealerships, shed brands and set timetables for profitability, showing that they – belatedly – realize that doing more to help themselves was necessary before pleading for federal help.

This is important, but lawmakers must ensure the companies follow through with, and in some cases improve, their plans in exchange for federal funds.

Last month, when auto executives used private jets to get to Washington, they asked for $25 billion. This week, when they traveled in hybrid cars, they say they need $34 billion. Chrysler and General Motors said they need cash now ($7 billion for Chrysler and $4 billion for GM this month with more to come); Ford said a $9 billion line of credit may be sufficient.

More important, the companies’ executives gave lawmakers blueprints for how they would trim costs in exchange for government help.

GM’s plan calls for a complete restructuring of the company and massive job cuts. Chrysler’s emphasizes the benefit of combining with another company. Ford’s is somewhere in between.

Many of the changes are largely symbolic. The companies’ three CEOs said they’d work for $1 a year (the millions they’ve made running the companies into the ground likely will sustain them). GM said it would cut its pay to top executives and Ford said it would cancel bonuses for management. Both Ford and GM said they’d sell their corporate aircraft.

More substantially, GM’s plan calls for cutting up to a third of its U.S. work force, more than 30,000 jobs, and closing 11 of its 48 North American manufacturing plants by 2012. It also proposes to drop 2,000 dealers and its Saturn, Pontiac, Hummer and Saab brands, while dropping the number of vehicle models from 63 to 40.

Ford, which is in the midst of restructuring, would focus on more fuel-efficient vehicles. It proposes to bring more fuel-efficient models from Europe for sale in the U.S. and speed development of electric vehicles. It said the company would be in the black by 2011.

Chrysler, which said it needs $7 billion just to make it to the end of the year, appears more focused on a sale of the entire company rather than remaking it. The company already has decreased its work force by more than 30,000 since 2007.

Union leaders said this week that they were willing to work with the auto companies to avoid their demise. A major concession could the scaling back or elimination of a jobs bank, which paid laid-off workers up to 95 percent of their salary while they were not working. Wages will be another sticky issue.

With more details, members of Congress now should be better able to decide if carmakers have appropriate plans to remake the industry to justify government help.