LIVERMORE, Calif. – R.C. and Stacy Davis lost their condominium to foreclosure in 2009, a bad break that seemed destined to keep them from buying another home for many years.

Yet only three years after their foreclosure, the couple recently signed the papers to buy a four-bedroom house in Livermore.

Their avenue to homeownership? A loan backed by the Federal Housing Administration.

“We’re as happy as can be,” Stacy Davis said.

The ability to get an FHA loan so quickly after a foreclosure could be welcome news to thousands of people who lost their homes during the housing bust.

While mortgage giants Fannie Mae and Freddie Mac make people wait seven years after a foreclosure, the FHA will approve loans after three years, providing the buyer has established good credit and the ability to pay the mortgage.

“There’s definitely a movement of folks who have had a foreclosure to re-emerge and re-engage in the market,” said Dustin Hobbs of the California Mortgage Bankers Association. He said brokers have picked up on the trend.

“It helps the housing market,” said Guy Schwartz of CMG Financial in San Ramon, Calif., which handled the Davises’ mortgage.

The FHA, which is self-supporting, provides mortgage insurance for loans with low down payments and more flexible household income requirements. The Davis loan came with a 3.5 percent down payment plus required monthly mortgage insurance and a 3.75 percent interest rate on a 30-year loan.

“An FHA loan is a good option for those who can qualify,” said Paul Leonard, California director of the Center for Responsible Lending. And there couldn’t be a better time to try, he said.

“We are at near substantial price corrections,” he noted. That and low interest rates present “kind of a historic opportunity if people can qualify,” he said.

The FHA said that it doesn’t have data on how many of the loans it insures involve buyers who have had foreclosures or short sales. Wells Fargo, the country’s largest FHA loan originator and servicer, said it doesn’t break out those loans. In the first six months of 2012, the bank made more than $73 billion in FHA loans, compared with $47 billion a year ago, spokesman Jim Hines said.

Mason McDuffie Mortgage in San Ramon is working with foreclosure victims. “We are making loans and have made loans to people who have corrected their credit,” said Bill Godfrey of Mason McDuffie. “It’s nice to see.”

The borrowers are “people who waited three years, have a job and qualify,” Godfrey said. “They have their credit, have a job, and things are looking better. They may not be perfect, … but that’s part of the way to move forward. Clearly there is some thawing in that area.”

FHA loans take a lot more time and work. “It’s a hard transaction to complete,” said Bob Barrie of Keller Williams in San Jose, noting that when he lists a home and there are multiple offers, a buyer with an FHA loan is at a disadvantage.