The parties involved in a class-action lawsuit over special education services in New Orleans are close to a settlement, according to new court filings, but details of any proposed agreement were not available Wednesday.

The Southern Poverty Law Center and a group of families filed the lawsuit in 2010, alleging that students with special needs had been shut out of the city’s public schools, were denied services to which they are entitled by law or were mistreated because of their disabilities.

The Orleans Parish School Board, which lost control of most of the city’s schools after Hurricane Katrina, is scheduled to discuss a potential deal in a closed-door meeting Thursday. The state-run Recovery School District, which took over the majority of the campuses, also will have to sign off on any agreement.

U.S. District Judge Jay Zainey has scheduled a follow-up meeting with all of the parties for Monday.

The case has been cited as evidence of a major failing in the city’s shift over the past decade toward independent charter schools, which have broad leeway to set their own policies without interference from a central district.

The types of complaints raised in the lawsuit were part of the impetus behind a central enrollment system, known as OneApp, that came online in 2012. Before then, parents simply went from one charter school to the next, looking for an open seat. If they couldn’t find a place, they were often assigned to one of the dwindling number of traditional schools, which ended up lagging in measures such as test scores and dropout rates.

Without any kind of central authority keeping tabs, charter schools faced accusations that they were simply turning away students with disabilities, hoping to avoid the extra costs involved.

Charter school leaders and their backers have vigorously denied cherry-picking students. But many of them also accepted the need for OneApp, hoping that it would put them beyond suspicion and simplify the enrollment process.