Mortgage bankers started a new effort Thursday to reform Fannie Mae and Freddie Mac, seeking to push Congress to pass legislation after a bipartisan group of senators failed in 2013.

The Mortgage Bankers Association released a new 60-page paper for moving the mortgage giants out of government custody. Under the bankers' plan, which adds details to a previously announced blueprint, the entities would act as regulated utilities providing guarantees for mortgage securities explicitly backed by the government and they could get new competitors.

The trade group hopes to begin swaying lawmakers on the plan now in hopes of seeing legislation passed next year, after Congress works on tax and regulatory reform.

David Stevens, the association's CEO, said the Senate Banking Committee is working toward reform now. "We've decided not to stand on the sidelines because ... the teams are out there," he told reporters Thursday.

The plan spells out in detail how Fannie and Freddie, which have been in government hands since 2008, could be transitioned from government custody to operating as utilities.

Failure to spell out how such as transition would work was one of the reasons that reform failed in 2013, Stevens said. Another was that the bipartisan legislation, authored by Sens. Bob Corker, R-Tenn., and Mark Warner, D-Va., did not contain an adequate plan for promoting affordable housing through the government-sponsored enterprises, a concern for liberal senators. The new paper addresses both of those points.

"There were deficiencies in providing good counsel" to lawmakers in 2013, Stevens said Thursday.

Senate Banking Committee Chairman Mike Crapo has said that reforming Fannie and Freddie is a priority for him in this Congress. Rep. Jeb Hensarling, his counterpart in the House, has made similar comments.

One major issue not addressed by the association, however, is how current shareholders in Fannie and Freddie would be treated in legislation. Many of those shareholders favor re-privatizing Fannie and Freddie and are locked in a legal battle with the government over change to the terms of the 2008 bailout in 2012 that sent all profits to the Treasury.