America's $11 trillion home-mortgage market is heading for a makeover.

Mortgage lending in the U.S. relies heavily on institutions set up in the 1930s by politicians and government officials seeking remedies for the Great Depression. Now, bankers say, the current economic crisis will force Congress and the Obama administration to decide how to repair or rebuild those institutions, including Fannie Mae, the Federal Home Loan Banks and the Federal Housing Administration.

The main focus is on the government-backed buyers of home loans: Fannie Mae, created in 1938, and its younger cousin, Freddie Mac, formed in 1970. Heavy losses stemming from mortgage defaults prompted regulators to seize control of the two companies Sept. 6. Though hobbled by those losses, Fannie and Freddie still buy or guarantee more than half of all home loans in the U.S.

The Treasury Department has agreed to provide them capital as needed, and the Federal Reserve said last week that it would spend as much as $600 billion buying debt and mortgage-backed securities issued by Fannie and Freddie over several quarters.

The consensus among both Republicans and Democrats is that the current structure of Fannie and Freddie doesn't work. Though they are owned mainly by private shareholders, they have a public mission to support the housing market. That has led to conflicts between shareholders' desire for maximum profits and congressional demands for more support to the housing industry.

A series of policy options compiled from various sources by Andrew Davidson, a mortgage-industry consultant, calls for turning Fannie and Freddie into cooperatives owned by the lenders that sell mortgages to them. These cooperatives would package mortgages into securities for sale to investors. Unlike Fannie and Freddie, the cooperatives wouldn't own large amounts of loans and related securities on their books. To make the securities more attractive to investors, Treasury would receive fees for agreeing to cover any losses on the securities above a certain level.

This explicit backing from Treasury would replace the current system under which investors merely assumed that the government would stand behind Fannie and Freddie. Many investors, especially those overseas, have lost confidence in that "implied" guarantee and want something definite.

This approach would take away from Fannie and Freddie their traditional duties of ensuring liquidity in the market by buying mortgage securities when other investors back away and of making special efforts to finance housing for poor people. If Congress sees a need for such functions, Mr. Davidson says, it should set up government programs to achieve them and allocate funds for those purposes.

A complication is that home builders and Realtors, both powerful lobbying groups, argue for a continuing federal role for Fannie and Freddie to ensure a steady flow of money into home mortgages, even when private investors recoil from the risk. Bank-controlled cooperatives, on their own, wouldn't provide the degree of support for housing that these lobbying groups want.

Rep. Barney Frank, a Massachusetts Democrat who is chairman of the House Financial Services Committee, will have a key role in this debate. He doesn't favor the status quo; the "hybrid system" of private shareholders and a public mission "didn't work well," he said in a recent interview. Rep. Frank said there may be a case for separating their current functions into different entities, one to finance housing that is affordable for low- and moderate-income people and another to ensure adequate funding for the mortgage market in general.

Congress also may tinker with the 12 regional Federal Home Loan Banks, which lend money to more than 8,000 commercial banks, thrifts, credit unions and insurers. These loans are a big source of funding for mortgages. But the home-loan banks also borrow based on an implied guarantee that no longer looks so attractive to many investors. Mr. Davidson says the home-loan banks may have to pay fees for an explicit government guarantee of their debt.

Write to James R. Hagerty at bob.hagerty@wsj.com

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