Donald Trump’s Treasury secretary nominee, former Goldman Sachs executive Steven Mnuchin, says he and the president-elect want to privatize the home-mortgage market and “will get it done reasonably fast.” That’s good news for American homeowners, the economy and taxpayers who were forced to foot the bill after the 2008 subprime mortgage meltdown.

For those familiar with global mortgage markets, this is not a radical proposal. The private sector provides mortgages in most major countries, and there is little difference in the share of homeownership between the U.S. and other developed countries. No other country has the equivalent of the private-public model of Fannie Mae and Freddie Mac—crony capitalism at its best.

The U.S. needs a new mortgage system that preserves the value that currently exists with Fannie and Freddie, never places taxpayers at risk again, promotes homeownership at affordable levels, and transitions to a new private model without disrupting the housing industry. Congress will also need to resolve the issues with shareholders of Fannie and Freddie resulting from the Obama administration’s unilaterally changing the terms of conservatorship in 2012 by seizing their capital and future profits.

Mr. Mnuchin won’t have to start from scratch. Positive steps have already been taken. Back office and securitization functions of Fannie and Freddie are being combined to increase efficiency. Fannie and Freddie’s huge portfolios are being reduced (albeit much of the reduction has been added to the Federal Reserve’s portfolio). The companies have also repaid taxpayers more than $240 billion against their $187 billion bailout.

Yet many politicians and industry participants believe that housing cannot prosper without government support. We disagree. The U.S. cannot afford to go through another financial crisis, which started with subprime mortgages and would never have been so large if the residential mortgage industry had been market-based.

Subprime mortgages have existed for decades. But they were a small percentage of the mortgage market until Fannie and Freddie reduced credit standards to increase their market share and meet low-income homeownership targets mandated by Congress. By 2007 nearly 50% of mortgages originated in the U.S. were subprime and “alt-A” types with government agencies guaranteeing about 70% of those, according to studies first conducted in 2011 by Edward Pinto of the American Enterprise Institute.

Without these government guarantees, the subprime bubble and financial crisis would have never happened. Bank regulators and industry experts warned Congress for decades about Fannie and Freddie and their increasingly large and risky portfolios, but Congress failed to act.

The solution is straightforward: The public-private hybrid of Fannie and Freddie—“government-sponsored entities”—should be abolished, their existing business sold or liquidated, and the mortgage market privatized. This can be done in a few easy steps.

The current $686,000 cap on new mortgages guaranteed by Fannie and Freddie should be reduced by $100,000 a year. This would put the companies out of originating new mortgages within seven years. The liability for outstanding guarantees should be managed by the current government conservatorship of Fannie and Freddie until they run off or are sold.

Some worry that this change may be too abrupt. But if the mortgage market doesn’t adjust fast enough, the process can be slowed by reducing the pace of the decline in the cap or making other tweaks. For example, if the government still wants to subsidize mortgages for low-income families and minorities, the cost should be on budget and transparent. The Federal Housing Administration already does this.

Others speculate that, without Fannie and Freddie, mortgage rates would skyrocket and the 30-year, fixed-rate mortgage would vanish. We disagree. Nonconventional or “jumbo” 30-year mortgages not guaranteed by Fannie and Freddie have existed for decades. In the decade preceding the financial crisis, the interest rate on these jumbo mortgages averaged only about 0.25% higher than similar guaranteed mortgages, a difference of a little over $40 a month on a $200,000 mortgage. Shouldn’t Americans, like homeowners throughout the world, pay a tax-deductible $40 extra a month so taxpayers aren’t on the hook for hundreds of billions to bail out Fannie and Freddie?

Private mortgages work around the world—including in Canada, the United Kingdom and other European countries—and have worked for decades on mortgages in the U.S. not guaranteed by Fannie and Freddie. There is no reason to believe they will not work for the entire U.S. mortgage market given America’s strong and deep capital markets.

It’s time for Congress to do what it should have done decades ago—give the Federal Housing Finance Agency clear direction to manage a smooth transition of the functions of Fannie Mae and Freddie Mac to the private sector. Get the government out of the mortgage business so taxpayers are never again at risk.