Treasury will boost its common stock stake in Ally to 74% from 56% under the deal outlined Thursday afternoon. Under the arrangement, Treasury will convert $5.5 billion of preferred stock to common shares.

The government emphasized that the deal will “accelerate Treasury’s ability to exit its investment in the company,” an important point at a time when the government is doing everything it can to paint the financial rescues of 2008 and 2009 as a win for taxpayers.

But by converting to common stock a large portion of the preferred stock Treasury received in propping the company up at the end of 2008, the deal also boosts a key measure of Ally’s financial strength.

The bank’s Tier 1 common ratio – measuring the proportion of stockholder capital available to absorb losses in a downturn – will rise to 9%, in line with the biggest U.S. banks, from 5% beforehand, officials said. That’s important as policymakers brace for another downturn in the U.S. housing market and possible knock-on effects on the car business, which is where Ally does much of its financing.

The government rescued GMAC, which was faltering thanks to its souring mortgage business and its ties to the collapsing auto industry, at the end of 2008.

Thursday’s announcement comes on the heels of a series of similar maneuvers by the government to show progress in extricating taxpayers from the bailouts that started in 2008 under the Bush administration. Treasury in recent weeks has held an initial public offering of General Motors (GM), sold the last of its common stock in Citigroup (C) and revamped for the umpteenth time its investment in AIG (AIG).

 “Our action today parallels the actions we took in converting Citigroup preferred stock and in the pending conversion of AIG preferred stock to common stock,” said Treasury Acting Assistant Secretary for Financial Stability Tim Massad.  “Our ultimate goal in all these investments is to exit as quickly as possible on terms that realize the most value for the taxpayer, and this transaction will facilitate that.”  

Under the arrangement outlined Thursday, Treasury will be left with $8.6 billion of preferred stock, some of which it will sell with help from Ally.

The news comes on the heels of another major development at Ally, which this week agreed to pay $462 million to settle a mortgage dispute with Fannie Mae (FNMA).

The terms struck some observers as surprisingly favorable to Ally and prompted Chris Whalen, who watches the industry for the Institutional Risk Analytics consultancy and has been on the lookout for backdoor subsidies to the banks, to call the deal “a gift from Uncle Sam,” which now controls Fannie.