SAN FRANCISCO — When San Francisco started trying to promote socioeconomic diversity in its public schools, officials hoped racial diversity would result as well.

It has not worked out that way.

Abraham Lincoln High School, for example, with its stellar reputation and Advanced Placement courses, has drawn a mix of rich and poor students. More than 50 percent of those students are of Chinese descent.

"If you look at diversity based on race, the school hasn't been as integrated," Lincoln's principal, Ronald J.K. Pang, said. "If you don't look at race, the school has become much more diverse."

San Francisco began considering factors like family income, instead of race, in school assignments when it modified a court-ordered desegregation plan in response to a lawsuit. But school officials have found that the 55,000-student city school district, with Chinese the dominant ethnic group followed by Hispanics, blacks and whites, is resegregrating.

The number of schools where students of a single racial or ethnic group make up 60 percent or more of the population in at least one grade is increasing sharply. In 2005-06, about 50 schools were segregated using that standard as measured by a court-appointed monitor. That was up from 30 schools in the 2001-02 school year, the year before the change, according to court filings.

The San Francisco experience is telling because after the recent U.S. Supreme Court decision restricting the use of race-based school assignment plans, many districts are expected to switch to economic integration plans like San Francisco's as a legal way to seek diversity. As many as 40 districts around the country are already experimenting with such plans, according to an analysis by Richard D. Kahlenberg of the Century Foundation, a nonpartisan public policy research group.

The purpose of such programs is twofold. Since income levels often correlate with race they can be an alternate and legal way to produce racial integration. They also promote achievement gains by putting poorer students in schools that are more likely to have experienced teachers and students with high aspirations, as well as a parent body that can afford to be more involved.

"There is a large body of evidence going back several years," Kahlenberg said, "that probably the most important thing you can do to raise the achievement of low-income students is to provide them with middle-class schools."

Economic integration initiatives differ from each other, and from many traditional integration efforts that relied on mandatory transfer of students among schools. It is difficult to measure how far students travel or how many students switch schools. The most ambitious effort and the example most often cited as a success is in the city of Raleigh, N.C., and its suburbs.

For seven years the district has sought to cap the proportion of low-income students in each of the county's 143 schools at 40 percent.

To achieve a balance of low- and middle-income children, the district encourages and sometimes requires students to attend schools far from home. Suburban students are attracted to magnet schools in the city; children from the inner city are sometimes bused to middle-class schools at the outer edges of Raleigh and in the suburbs.

Only 40 percent of black students in grades three through eight in Wake County, where Raleigh is located, scored at grade level on state reading tests in 1995. By the spring of 2006, 82 percent did.

"The plan works well," said John H. Gilbert, a professor emeritus at North Carolina State University in Raleigh who served for 16 years on the county school board and voted for the plan. "It's based on sound assumptions about the environment in which children learn."

San Francisco had been under a court order to desegregate for more than 20 years, with no school allowed to have a majority of students from one racial or ethnic group. But after Chinese-American parents whose children were kept out of certain schools sued, the district switched to a plan that sought socioeconomic diversity.

Students apply to the schools they want to attend, and the district uses a "diversity index" for assignments when a school is oversubscribed. The index considers the language spoken at home, whether a child qualifies for free lunch or is in public housing, a child's academic performance and the quality of a child's prior schools. But it has not resulted in racial integration.

"We were hopeful that the diversity index would work," said Stuart Biegel, a law professor at UCLA who was the district's court-appointed monitor. "No one was rooting against it. But it didn't work."

Officials say one problem is that many students apply to neighborhood schools that do not recruit enough students from outside their area. Another problem is demographics. Biegel said public school students in San Francisco were relatively low income overall, whatever their race or ethnicity, so the diversity index produced less mixing than hoped.

David Campos, the general counsel to the school district, said the resegregation was so disappointing that the school board might try to test whether Justice Anthony M. Kennedy's opinion in the recent Supreme Court case left open the possibility of using race if other methods of integration fail.

"We stopped using race at some point," Campos said. "And then for a number of years we have tried to use a number of race-neutral factors to achieve racial diversity, which methods haven't worked. Should the board decide to use race, and they may or may not, we are a very good test case."