As state and federal authorities announced the details of their $26 billion mortgage settlement with big banks on Thursday, millions of American homeowners were hoping that this time they would finally get relief.

Some, like Jessica Cooper of Toledo, Ohio, will discover the program’s limitations.

Since she was laid off in June 2009, Ms. Cooper and her husband have been pressing Bank of America to modify the terms of the $112,000 mortgage on their home. But because the loan is owned by the Federal Housing Administration, it is not covered. Similarly, Carlos Sandoval de Leon has been seeking a break from Wells Fargo on the $662,000 he owes on a Brooklyn brownstone. But because that mortgage is held by a private investor, it too falls outside the scope of the agreement, which mostly covers loans held by the banks themselves.

The bulk of the settlement, about $20 billion, would go to one million American homeowners who would have their mortgage debts reduced or their loans refinanced at a lower interest rate. It also includes $1.5 billion for roughly 750,000 people who lost their homes to foreclosure between 2008 and 2011, with each receiving between $1,500 and $2,000.

Economists do not expect a big boost for the economy, in part because the banks have three years to distribute the aid. Some experts questioned whether the accord would do much to stabilize the housing market and its glut of millions of foreclosed homes.