Officials in Shelby County, Tenn., complain they’ll have to spend millions to satisfy a federal judge’s ‘‘arbitrary’’ desegregation order. It’ll mean busing minority students up to an hour away and replacing hundreds of white teachers with black ones, they say.

In Huntsville, Ala., under a similar court order, students can transfer from a school where they’re in the racial majority, but not the other way around.

And in the Tucson, Ariz., Unified School District, students could move from one school to another only if the change improved ‘‘the ethnic balance of the receiving school and (did) not further imbalance the ethnic makeup of the home school.’’

But wait: Hasn’t the U.S. Supreme Court consistently moved away from using race as a factor in deciding where kids should go to school?

Didn’t the high court recently put an exclamation point on that trend, ruling that two districts’ heavy reliance on race in student assignment policies violated the Constitution’s guarantee of equal protection?

Yes, and yes. But there are still hundreds of districts across the country, from the Northeast to the Southwest, that operate under federal court desegregation orders — some more than four decades old.

These districts are in a unique and sharply debated position with respect to the Supreme Court’s rulings. They exist in what critics consider a historical Twilight Zone, where federal judges can make seemingly contradictory decisions.

‘‘So which ruling do I violate?’’ asks a perplexed Bobby Webb, superintendent of schools in Shelby County, where Memphis is located. ‘‘The judge’s ruling now, or the earlier rulings that we can’t discriminate against people on the basis of the color of their skin?’’

Front-page court battles over integration are mostly a thing of the past. But according to the U.S. Department of Justice’s Civil Rights Division, there are at least 253 school districts still under federal court supervision in racial inequality cases — and those are just the ones in which Justice intervened.

Many of the more infamous names — Boston, Little Rock, Charlotte, N.C. — are gone from the list, having satisfied judges with their desegregation efforts and being granted what’s called ‘‘unitary status.’’ In the last two years alone, at least 75 districts have won such status.

Of those that remain, most are in the South. Georgia leads with 61, followed by Mississippi with 51, Alabama with 50 and Louisiana with 30. But long-standing cases are still pending in places like Arizona, Connecticut, Indiana and Illinois.

The question of these districts came up this past year as the Supreme Court heard arguments involving voluntary diversity plans in Seattle and Louisville, Ky.

In June, the court ruled that student assignment policies in those two districts relied too heavily on individual students’ races and, so, were unconstitutional. But in those two districts there were no orders to remedy past state-sponsored segregation.

On the other hand, districts operating under integration orders may set policies that explicitly consider race. Justice Ruth Bader Ginsburg acknowledged the ‘‘anomaly’’ of demanding that such districts work diligently toward racial integration, but once it’s achieved mandating that race be ignored.

‘‘What’s constitutionally required one day gets constitutionally prohibited the next day,’’ she said. ‘‘That’s very odd.’’

Others have expressed confusion and frustration.

In Memphis, the school board and the NAACP Legal Defense Fund filed a joint motion to end 44 years of court oversight. The Department of Justice joined in, writing that on the whole, the district had ‘‘complied in good faith with its obligations’’ under the desegregation orders.

U.S. District Judge Bernice Bouie Donald disagreed strongly.

The old court orders require districts to dismantle ‘‘all vestiges’’ of government-sponsored segregation. A district must show compliance in six areas: student body composition, faculty, staff, facilities, extracurricular activities and transportation — the so-called ‘‘Green factors,’’ from a landmark Virginia case with a plaintiff by that name.

While Donald agreed that Shelby County had achieved integration in school staffing, transportation and facilities, she ruled the district was still woefully deficient when it came to student and faculty assignment.

Of the district’s 46 schools, she noted, only 17 had a racial makeup that was reflective, within 10 percentage points, of the 32 percent black student population. And when the new Southwind High School opened its doors this fall, it was around 95 percent black.

After making considerable progress, she wrote in late July, ‘‘the County has seemingly drifted from any serious focus on desegregation.’’

Donald ordered that the racial composition in each school, ‘‘of both faculty and students,’’ mirror the overall student population, within 15 percentage points. She also announced the appointment of a special master to oversee the plan’s implementation, and suggested the district could remain under supervision until 2015.

The board asked for a stay, arguing that meeting Donald’s ‘‘arbitrary’’ demands would force the district to hire hundreds of new black teachers and bus 9,000 pupils — or about 20 percent of the total student population — for up to an hour a day at an additional cost for transportation alone of more than $1.6 million a year.

Board attorney Valerie Speakman says Donald’s order ‘‘flies in the face’’ of 40 years of Supreme Court precedent.

Board chairman David Pickler, also an attorney, terms Donald’s requirements ‘‘destructive’’ of district integration efforts, saying they’d force the busing of black students past the ‘‘state of the art’’ Southwind to an older, inferior school.

Across the country in Tucson, another judge has been accused of misapplying the June high court ruling in a 29-year-old desegregation case.

In August, U.S. District Judge David C. Bury cited the decision in declaring the district’s Policy 5090 unconstitutional. Adopted at a time when Anglos constituted the student majority, it now has the effect of limiting the options of minority students.

Between November 2006 and this past September, 1,108 transfer requests were denied because they would have upset the racial balance at schools, says a district administrator, Pam Fine.

Bury found that Policy 5090 ‘‘relies on the race of the student in a non-individualized, mechanical way.’’ Although not granting full unitary status, Bury says he anticipates the district will be able to prove that all vestiges of forced segregation in student assignment ‘‘have been eliminated to the extent practicable.’’

Following Bury’s ruling, the district scrapped 5090, reopened the enrollment process and sent transfer invitations to 695 households that had been turned down. Only 113 transfers were requested, mainly because families didn’t want to move their children three weeks into the school year, Fine says.

Rubin Salter Jr., attorney for the plaintiffs, says the June Supreme Court ruling does not fit the facts in Tucson and asked that the transfer policy be reinstated. Bury denied the request.

Being under court supervision doesn’t guarantee a district will be the picture of integration.

In the Huntsville system, the student population is 43 percent black. Yet despite 44 years of court supervision, more than half of the district’s four dozen schools are majority minority — and nine schools are above 90 percent black.

‘‘Judges just kind of let the school district evolve,’’ says Gary Orfield, co-director of The Civil Rights Project at UCLA.

Under Huntsville’s court-approved choice plan, students are allowed to transfer from a school in which they are in the majority racially to one where they would be in the minority. But Superintendent Anne Roy Moore concedes that few, if any, of the 306 transfer requests approved last year were from white kids.

‘‘It’s designed to go both ways,’’ she says.

The Justice Department has contacted Huntsville about seeking unitary status. During a briefing, attorney J.R. Brooks told the school board there might be some ‘‘pain’’ involved.

‘‘If the Green Factors were strictly enforced, then there would be some issues about rezoning and reassigning’’ students and teachers, he told the AP in a telephone interview. ‘‘It could be disruptive.’’

Moore, who is black, says some of her most racially homogenous schools are among the highest performing — and will remain so if court supervision ends.

‘‘I think that when you become unitary, the expectation is that you still will uphold the spirit of the law or the integration and that you’ll work to end any discriminatory practices,’’ Moore says. ‘‘Because, in reality, a group that had brought suit, say, 30 years ago could still step up and do that again.’’

But Orfield says that’s not so: A grant of unitary status ‘‘ends the rights of the minorities in your community to ever have the court intervene on the basis of a history of discrimination.’’

In the Tennessee case, Judge Donald acknowledged that ‘‘a district cannot be held responsible for maintaining such balance in perpetuity in the face of demographic forces beyond its control.’’ But she said the Supreme Court’s rulings ‘‘underscore the momentous, irreversible nature of this Court’s pending decision as to whether the County has achieved unitary status.’’

Shelby County is appealing to the U.S. 6th Circuit Court of Appeals.

‘‘It just seems extremely absurd for her to dictate rules to us that are against the federal law,’’ says Webb, the superintendent.

No, she is simply making the district touch all the bases before heading for home plate, says Robert Pressman, a former Justice Department attorney and veteran of Boston and other desegregation fights. ‘‘The judge is taking a stand,’’ he says.

While there is a certain stigma attached to being under court supervision, Orfield says school administrators who value diversity shouldn’t be in any hurry to get out from under these orders.

‘‘What you get from it isn’t freedom,’’ he argues. ‘‘School districts without court orders don’t have freedom to do what they are doing’’ to maintain racial diversity.

Maree Sneed doesn’t see it that way.

In a memo to the districts she represents, the Washington, D.C., attorney noted that five of the justices indicated that they view ‘‘avoiding the harms of racial isolation and providing the educational benefits of diverse student enrollments to be compelling governmental interests.’’ If race is used in a narrowly tailored way to achieve one of those goals, she wrote, ‘‘a number of race-conscious practices … are likely permissible …’’

Each community must decide how important school diversity is, and how best to achieve it in this new judicial climate, she says.

‘‘The goal should be to become unitary,’’ Sneed says. ‘‘Because you’re trying to fix a dual system.’’