The newly cooperative Bank of America (BAC) set off a big bank stock rally Monday by resolving some worries about the cost of its bubble-era bad lending antics.

BofA agreed to a $2.8 billion settlement of mortgage-repurchase claims by the government-sponsored housing companies Fannie Mae (FNMA) and Freddie Mac (FMCC).

Shares of BofA, the nation’s biggest lender by assets and the biggest mortgage servicer as well, rose 5% after the bank announced the plans. The other big mortgage banks, JPMorgan Chase (JPM), Wells Fargo (WFC) and Citi (C), rose 2%-3% as well.

This despite the fact that Monday’s settlement doesn’t address the lion’s share of the banks’ exposure to mortgage putback claims.

Most of the mortgages covered in Monday’s deal were written by Countrywide, the notorious subprime lender that BofA acquired in a 2008 fire sale, between 2004 and 2008.

Under the arrangement, BofA cleared out what execs called a growing pipeline of mortgage putback requests from Fannie, which had much closer ties with Countrywide than did Freddie. The bank also reached a settlement covering all its deals with Freddie. In both cases, the mortgage investors accused BofA of failing to properly execute the mortgage loans – known in the industry as representations and warranties claims.

Wall Street applauded the deal because it cost less than investors had expected and raises hopes that all the big banks will soon settle with Fannie and Freddie, which finance most house purchases by buying loans and mortgage-backed securities from the banks. Ally Bank, the government-owned car lender, announced a settlement with Fannie last month.

Monday’s agreement “shows a willingness of Bank of America to take more control of the situation, and sets a tone for the year by having this move announced on Day 1 of the new year,” said CLSA analyst Mike Mayo.

Even so, the bigger questions about the banks’ exposure to mortgage litigation remain unaddressed. BofA said last month it is in talks with a group of mortgage investors about their request that the bank repurchase billions of dollars in so-called private label loans – those that weren’t sold to Fannie or Freddie.

As badly as Fannie and Freddie have done in recent years, it is indisputable that private label loans have been defaulting at a much higher rate, which means the banks may face bigger losses as they try to clean up that swamp.

BofA financial chief Chuck Noski said on a conference call Monday that the bank will continue to “vigorously defend” itself against such claims. He said investors shouldn’t conclude from Monday’s announcement that private-label settlements are on the way.

That’s an important caveat, because the bank’s potential losses in the private label disputes could dwarf the $6 billion or so BofA has now recognized in losses on putbacks by Fannie and Freddie.

Deutsche Bank analyst Matt O’Connor says investors can expect BofA to face $15 billion or so of costs on the private label securities, though that process will likely play out over months and years, rather than being settled all at once.

“The big unknown remains private label risk — which will take a while to play out,” he writes.

BofA is due to post its fourth-quarter numbers Jan. 21. Noski said the bank will then provide investors with more information on the size, scope and performance of private label securitizations.