Correction: An earlier version of this article incorrectly said that proposals by Rep. Darrell Issa (R-Calif.) and Elijah E. Cummings (D-Md.) would drop a retiree health payment. The Postal Service would still be required to make an annual payment to fund health benefits for future retirees. The article also included a potentially misleading reference to doing away with the payment. As the story went on to say, the proposals would replace the current $5.5 billion payment with a payment based on actuarial calculations.

The architect of a forthcoming House bill to restructure the financially ailing U.S. Postal Service said Wednesday that he’ll strike language to force labor unions to open existing contracts and eliminate no-layoff rules.

The change of heart from Darrell Issa (R-Calif.), chairman of the House Oversight and Government Reform Committee, is a big concession to labor and its Democratic allies in Congress, who will be key to getting a bill through Congress.

At a hearing on a new round of House proposals to stabilize postal finances, Issa said he hopes a plan will clear his committee before Congress breaks for its annual August recess.

The Postal Service has struggled to stay financially solvent as mail volume has plummeted, a casualty of the digital age. The agency also has been hamstrung by a $5.5 billion annual payment for health benefits for future retirees, defaulting on two payments in the past year.

Postmaster General Patrick Donahoe said the payment results in a layout of $10,000 for health care for retirees over 65, “when we should be paying $3,500.”

Lawmakers could not agree on a restructuring plan in the previous Congress, with the House failing to bring a Senate-passed bill to the floor.

Issa and Elijah E. Cummings (D-Md.), the committee’s ranking member, are now striking more common ground. Both expressed a sense of urgency to move forward.

They agree on doing away with the health payment and instead requiring that the Postal Service pay what it will owe retirees for their costs. The change could reduce expenses for current and future retiree benefits by between $2 billion and $5 billion, from $8.5 billion, committee aides said.

But tension continues over whether to scratch Saturday delivery of letters and magazines. The move would save $2 billion a year but is opposed by unions, many lawmakers representing rural districts and some private mailers.

Donahoe recently tried to drop Saturday mail delivery without congressional approval but was forced to back down.

Issa is calling for five-day delivery and a halt to curbside mail delivery in favor of clustered boxes on street corners, a change he says could save at least $4 billion annually.

Donahoe said each door-to-door delivery costs $353, compared with $161 at a cluster box. But Cummings, who introduced his own bill Wednesday, opposes both changes because they would cost jobs.

The Postal Service already has cut retail hours at thousands of post offices and shut hundreds of mail-sorting hubs. Cliff Guffey, president of the American Postal Workers Union, said the downsizing is starting to slow mail delivery.

“We’re at the point now where the more right-sizing we do, the more the mail is delayed and it loses its value to the customer,” he said.

A bill from Cummings would allow the Postal Service to bring in new revenue from beer and wine delivery and other services and require the agency to hire a chief innovation officer to come up with nonpostal products.

He would cap executive pay and scrap bonuses if budget-balancing targets aren’t reached. His bill also would allow the agency to continue to offer buyouts through 2016.

Issa said Wednesday that his bill will include only a prospective ban on no-layoff contracts.

Both plans would restructure debts for future retirees. But Cummings would give postal officials access to pension surpluses to pay off a range of debts, while Issa would not.