A key question in the raging debate over school segregation is how much the personal choices of white and wealthy parents contribute to the isolation of poor children of color in separate and often subpar schools.

A new paper sheds light on exactly that. The study, by Steven Glazerman and Dallas Dotter of Mathematica Policy Research, took advantage of the school lottery system in Washington, D.C., which allows families to apply for classroom seats outside of their neighborhoods. Past research shows that when asked, American parents claim that academic performance is their greatest priority when selecting schoola for their children. But Glazerman and Dotter were looking for “revealed” preferences: the conclusions that could be drawn not by talking to parents, who might feel pressured to give socially acceptable responses, but by examining how 22,000 applicants of varying races and classes actually ranked 91 public charter schools and 110 district schools, at the pre-K, elementary school, middle school, and high school levels.

The researchers tested a broad range of factors that could explain why parents choose a school: its proximity to a family’s home, test scores, after-school activities, uniform policies, class size, the crime and income levels of the surrounding neighborhood, and the racial and socio-economic makeup of the school’s student body. Only three of these factors significantly drove parental choice. Parents preferred high test scores, schools closer to home, and schools where their own child would be alongside more peers of his or her same race and class.

Across race and class, a middle-school parent was 12 percent more likely to choose a school where his child’s race made up 20 percent of the study body, compared with a school with similar test scores where his child’s race made up only 10 percent of the study body. White and higher-income applicants had the strongest preferences for their children to remain in-group, while black elementary school parents were essentially “indifferent” to a school’s racial makeup, the researchers found. The findings for Hispanic elementary and middle school parents were not statistically significant.

The study also demonstrated white parents’ taste for what the journalist Nikole Hannah-Jones has termed “carefully curated integration,” the kind that exposes white children to some poor peers of color but not “too many.” At the elementary-school level, white Washington parents prioritized schools where about 60 percent of the student body was white and were slightly more likely to avoid schools with larger percentages of white children. At the middle school level, the researchers found that the “bliss point” for white parents was a student body that was 26 percent white. In a district where 73 percent of students are black, 14 percent are Hispanic, and only 9 percent are white, such preferences contribute to a significant clustering of white children, which results in black and Hispanic students being further segregated. (The researchers were able to isolate race from other factors, like location and test scores, so these racial preferences appear to operate independently of other factors parents look for in a school.)

Glazerman and Dotter’s work has big implications for policymakers as more districts across the country embrace school choice, allowing parents to select charter, magnet, and themed schools outside their neighborhoods. For instance, the researchers found that Washington’s lottery system slightly increases racial segregation in the elementary grades; if parents simply enrolled their young children in schools closest to home, black, white, and Hispanic elementary-school kids would be less clustered (though looking at class separately from race, the study found that poor children would be more segregated in a purely geography-driven system).

The most effective way to increase integration, the researchers posit, would be to move toward a theoretical system of “unrestricted choice,” in which the most desirable schools have an unlimited number of seats, while less desirable schools shut down. In the real world, that is a difficult, if not impossible, policy to enact. No school has unlimited space. And cities across the country have been riven in recent years by controversies over whether to expand the number of charter school seats, close low-performing schools, or turn them over to new managers. Communities often fight to keep struggling schools open. Despite low test scores, such schools are repositories of neighborhood history and pride.

Ultimately, parental choice alone cannot rectify school segregation, which is also driven by housing segregation and the too-rigid boundaries between school zones. Last month, the Obama administration announced changes to the Section 8 housing voucher program that could make it easier for poor renters to afford homes in higher-income neighborhoods and suburban towns. Just this week, Sen. Chris Murphy (D-Conn.) and Rep. Marcia Fudge (D-Ohio) introduced the Stronger Together Act, which would devote $120 million to encouraging school desegregation. The funds could support new magnet schools open to children from both cities and their surrounding suburbs, which would lead to more integration. And the Department of Education announced in April that it would offer modest grants to school districts that try to increase racial and socio-economic diversity.

The amount of federal money proposed for these efforts is paltry, even if Republicans were to defy expectations and support the Stronger Together Act. Still, these moves are a good start. Because research—and history—show that left to their own devices, parents won’t desegregate schools.