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

The change from House Committee on Oversight and Government Reform Chairman Darrell Issa (R-Calif.) is a major concession to labor unions and their allies among Democrats in Congress, who will be key to getting a bill through Congress.

Speaking at a hearing on a new round of House proposals to stabilize postal finances,   Issa said he hopes to get a bill out of his committee before Congress breaks for its annual August recess.

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

Postmaster General Patrick Donahoe said the prepayment results in $10,000 in health payments for retirees over 65, “when we should be paying $3,500.”

Lawmakers failed to reach agreement on a restructuring plan in the last Congress, with the House failing to bring a Senate-passed bill to the floor.

Issa and Democrat Elijah Cummings (D-Md.), the committee’s ranking member, have struck more common ground than before, and both expressed a sense of urgency to get legislation through Congress.

Cummings and Issa agree on the need to do away with the prepayment for health benefits and require instead that the Postal Service pay what it will owe.The expenses for current and future retiree health benefits would drop from $8.5 billion to between $2 billion and $5 billion, committee aides said.

But tension continues over  whether to eliminate Saturday delivery for letters and magazines, a move that would save $2 billion a year but is opposed by labor unions, many lawmakers representing rural districts and some private mailers. Issa is calling for five-day delivery as well as a halt to curbside delivery of the mail in favor of post office boxes or 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 to $161 for delivery to a cluster box. But Cummings, who introduced his own bill Wednesday, opposes both changes because they would cut jobs.

The Postal Service already has reduced retail hours at thousands of post offices and closed hundreds of mail-sorting hubs. American Postal Workers Union President Cliff Guffey said the closings are already slowing 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.

Cummings’ bill 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 non-postal products.

Cummings would cap executive pay and scrap bonuses if budget-balancing targets aren’t reached. He would urge the Postal Service to reduce its workforce but not nullify existing bargaining agreements to do it. His bill would allow the agency to continue to offer buyouts through 2016.

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

Both proposals also seek to restructure debts for future retirees. But Cummings’ proposal would give postal officials access to pension surpluses to pay off debts, while Issa’s would not. Both lawmakers would also lift rate caps for some classes of mail, particularly periodicals, that now pay artificially low mailing costs.

The proposals come on the heels of a failed attempt by Donahoe to drop Saturday mail delivery without congressional approval. Donahoe said he was acting in desperation because Congress failed to approve a restructuring plan for the mail agency, which lost $15.9 billion last year.

He was forced to back down after lawmakers objected.