A program meant to improve diversity at the city’s specialized high schools is poised to slightly increase black and Hispanic enrollment, according to data released Wednesday, though the program continues to be dominated by Asian students.

The Discovery program offers admission to students from high-need families who just missed the exam cutoff and who agree to attend a summer program. In recent years, the initiative has helped more white and Asian students gain admission to eight city high schools that determine admission based on a single test.

But as part of a broader overhaul of specialized high school admissions, including a push to eliminate the exam, officials changed the eligibility criteria this year so that only needy students from high-poverty schools could qualify. They also expanded the number of seats awarded through Discovery.

Those changes appear to have boosted black and Hispanic offers: 30 percent of the 922 offers issued through Discovery went to those students, up from 22.4 percent the previous year. (Roughly 67 percent of the city’s students are black or Hispanic.)

The changes also appear to have benefited Asian students, who saw the largest gains and already make up the majority of students at specialized schools — despite representing 16 percent of the city’s students. This year, 54 percent of Discovery offers went to Asian students, up 11 percentage points. White student offers fell about 12 percentage points to 14.6 percent.

Still, those changes are unlikely to make much of a dent integrating the specialized high schools, which captured national headlines after just seven black students were accepted to Stuyvesant, the most selective of the city’s elite high schools. For one, Discovery is projected to represent only about 13 percent of seats at specialized schools this year, meaning that even if that pool of students is more racially diverse, it won’t have a large overall effect. It’s also unclear which students will accept offers through the program.

Even under the city’s forecasts, changes to the Discovery program alone will only boost black and Hispanic enrollment to 16 percent, up from 9 percent now, a reality Schools Chancellor Richard Carranza acknowledged in a statement.

“We’re using every tool at our disposal to increase diversity at the specialized high schools, but despite the incremental progress we’re making through the Discovery program, the status quo remains the same,” he said. “We need to eliminate the test now.”

The city’s broader push to eliminate the single exam in favor of admitting top students from every middle school — a proposal that has yet to be approved by state lawmakers and has attracted strong opposition in some quarters — would have a more sizable effect.

The latest statistics may also have implications for a civil rights lawsuit that argues the latest version of the Discovery program discriminates against Asian students. That argument may be harder to make now, since Asian students’ offers through Discovery increased this year.

The Pacific Legal Foundation, which filed the lawsuit, declined to comment Wednesday.

“This is definitely not the impact that the Pacific Legal Foundation and the plaintiffs suing the city were saying about Asian American students,” said Vanessa Leung, who helps run the Coalition for Asian American Children and Families. “I think for us, it was like, see, the sky is not falling.”

Christina Veiga contributed reporting.