If you missed out on Washington’s cash incentive program to trade in your old clunker, Uncle Sam still has a deal for you: The government will sell you rejects from its own fleet, even as it makes dealers scrap all those old cars that were collected from the public.

The sale of the federal castoffs at auction is nothing new; deals for the consumer mean income for the government. But in swapping out old government cars for new models under the economic stimulus package, officials also are claiming environmental benefits that don’t add up.

The General Services Administration used stimulus money to buy 17,246 new vehicles, including more than 3,000 hybrids, for an impressive 40 percent improvement in fuel efficiency over the old models, the agency says. It said that translates into a decline of 334 million pounds of greenhouse gases in the atmosphere over the next seven years, the difference between the emission levels of the old cars and their replacements.

There’s no question the federal fleet is greener. But the environmental claim doesn’t take into account that most of the old wheels still will be on the roads, driven by people who bought them at auction.

Just how that affects the environment depends on the gas mileage of the auctioned cars and whether buyers stopped driving worse clunkers when they bought government hand-me-downs. Mileage driven by new owners and government drivers also is a factor.

GSA officials said in a statement that greening the federal fleet helps the environment in any event and fulfills the agency’s “mission to serve as a responsible steward of taxpayer dollars and assets.”

“At a value of approximately $40 million, the government-owned replaced vehicles will not go to waste,” the agency said. “They will be resold to further invest in greening the federal fleet.”

The auctions differ from the Transportation Department’s wildly popular, $3 billion Cash for Clunkers program that junked nearly 700,000 trade-in vehicles traded in by the public this summer. The government paid people up to $4,500 to trade in cars getting 18 miles per gallon or less.

Both the green fleet and Cash for Clunkers programs were part of the $787 billion Recovery and Reinvestment Act to stimulate the nation’s economy through sales of new American cars. The Obama administration touted environmental improvement as a companion goal.

Such programs can encourage automakers to speed fuel economy improvements, environmental advocates say, but are far less potent than the anticipated impact of President Barack Obama’s broader strides in regulating greenhouse emissions and hastening fuel economy improvements.

The GSA’s $300 million in stimulus money replaced each older car, truck or bus with a new model offering better fuel efficiency. The agency has not yet disclosed the models and fuel efficiency details that produced the claimed 40 percent fuel efficiency improvement.

The trade-ins, from agencies as diverse as the Marine Corps and the Smithsonian museums, are still serviceable, said GSA officials who were authorized to talk to The Associated Press on condition their names not be used. As many as 8,000 vehicles have been auctioned off so far, they said.

Aside from those live auctions, GSA runs an online auction that sells 40,000 vehicles a year, from beat-up Forest Service pickups to FBI sedans.