An unusual congressional hearing on the District’s finances proved more benign than some local activists had feared Thursday, as Mayor Vincent C. Gray and D.C. Council Chairman Kwame R. Brown visited Capitol Hill for a relatively cordial session that mostly avoided controversial topics.

Rather than raising the specter of the return of the federally mandated Financial Control Board, which was not discussed, the hearing offered some hope that the District could soon see its budget partly uncoupled from the slow and unpredictable federal appropriations process.

The hearing before the subcommittee of the House Oversight and Government Reform Committee that handles D.C. issues comes at a time when mistrust of Congress is running high in some quarters of the District. President Obama approved a spending deal last month that prevents the District from spending its own money to fund abortions for low-income women and also revives and expands a private school voucher program that has divided local officials.

But though the voucher program and a few other conflicts came up Thursday, the hearing mostly centered on fiscal policy. There was no mention of any recent city scandals, such as allegations by former mayoral candidate Sulaimon Brown that he was promised a city job in exchange for backing Gray, or Kwame Brown’s efforts to procure a “fully loaded” SUV for his official use.

“It wasn’t negative at all,” Gray (D) said after his appearance. “I thought it was a good discussion.”

During his testimony, Gray hammered repeatedly at the theme that the District needs budget autonomy.

Complaining that “the District’s appropriation is often caught up in national policy disputes that typically delay our local budget enactment and that do not have anything to do with the District,” Gray said that “it’s time” for approval of the city’s budget to be removed from the appropriations process.

Rep. Darrell Issa (R-Calif.), chairman of the full oversight panel, offered surprising news on that subject later in the hearing, after Gray and Brown (D) had left.

“I’m reasonably confident that no, we cannot accept budget autonomy fully,” Issa said, “but I am going to be offering an alternative that . . . provides a mechanism for a separate vote, separate consideration of District funds.”

Under Issa’s plan, Congress would approve what he called a “contingent budget” for the District that covers only locally raised tax funds. Then, later in the year, the House and Senate would pass federal appropriations for the District as usual.

“I think by bifurcating them . . . we can do it early on in every Congress and do it separate from a sometimes-difficult [federal] budget process,” Issa said.

Natwar M. Gandhi, the District’s chief financial officer, and Alice M. Rivlin, the former head of the Financial Control Board, responded positively to the proposal.

“I think this would be possible and a very good idea,” Rivlin said.

Del. Eleanor Holmes Norton (D-D.C.), the chief advocate for D.C. budget autonomy on the Hill, sounded surprised by Issa’s suggestion. “This is the first I’ve heard of it, but it’s something I’d very much like to work with him and build on,” she said.

In a statement issued Thursday afternoon, Norton praised Issa’s proposal, saying it “would appear to significantly improve the District’s ability to manage its finances and operations.” But her news release also warned that the “proposal has some drawbacks,” noting that it would give Congress “two annual opportunities to interfere with the District’s local budget.”

In the hearing Republicans made multiple comments about the District’s Opportunity Scholarship Program. The school vouchers are supported not only by congressional Republicans but also by Brown and several recent District mayors. Norton is an outspoken opponent of the program.

“The gentlelady from the District of Columbia does a good job representing a point of view of the District, but . . . there are more views in the District than just hers,” Issa said.

Rep. Trey Gowdy (R-S.C.), a freshman lawmaker who chairs the D.C. subcommittee, acknowledged that he was still getting to know the area and thanked Gray for “introducing me to your beautiful and magnificent city.”

Gowdy acknowledged that every city and local government faces economic challenges similar to the District’s.

“Heaven knows the United States Congress is struggling with its fiscal responsibilities,” he said.