Some Head Start and children’s services centers have used city Department of Education money to create new seats for children whose parents’ incomes are too high to qualify for subsidized care. But because of complex reporting requirements, these centers tend to separate children according to their eligibility. At some schools, there is an “A.C.S. room” for the children of the working poor and a “U.P.K. room” for better off children who are not eligible for subsidized care.

A few child-care centers, despite the obstacles, successfully mix children of different economic classes. At the Park Slope North-Helen Owen Carey Child Development Center in Brooklyn, for example, children learn together in what are called “blended classrooms.” The Administration for Children’s Services has officially promoted this model of integration for a number of years, but few centers have managed to pull it off. In fact, the city Department of Education told Park Slope North that subsidized children had to be in separate pre-K classrooms in the 2014-15 school year. When staffers insisted on blended classrooms anyway, the center received less funding.

It doesn’t have to be this way.

First off, the city should enable blended funding, as it has promised to do this fall. But it should also help centers complete complex paperwork required to combine Children’s Services, Head Start and Department of Education funds.

The city should offer more pre-K classes in public schools in economically mixed neighborhoods. Roughly 40 percent of pre-K seats are in ordinary public schools, charter schools and new free-standing “pre-K centers” operated by the Department of Education. These are open to all, regardless of income. A few, like the new K280 center in the Windsor Terrace section of Brooklyn, welcome children from different neighborhoods. Providing or subsidizing transportation would encourage parents to try a school outside their neighborhood and would probably lead to better integration.

The rapid increase in pre-K enrollment is a huge achievement. But ensuring quality is just as important, and programs that are economically stratified are rarely of equal quality. Mr. de Blasio’s pre-K initiative holds the potential to break down the economic segregation that has long bedeviled public and private preschool, but this once-in-a-generation opportunity will be lost unless his administration takes aggressive steps to create more economically diverse classrooms.