The House of Representatives is slated to consider an overhaul of the bill this month, and Senate legislation is moving forward in committee. Many contentious issues are at play—from student testing to teacher accountability—but among the biggest to emerge is the question of whether federal funds dedicated to help low-income students should be allowed to follow those students to schools they choose. As No Child Left Behind currently stands, that money is allocated toward the schools that enroll the students rather than the students themselves.

The battle lines have been drawn, with Republicans generally favoring "portability" of such federal money, or Title I funding, for low-income students as a way of injecting choice and market forces into public education. Democrats are mostly opposed to portability because the move would shift money from poor schools to rich ones, tilting the playing field against low-income students.

But it’s time to move beyond this familiar back and forth and entertain a grand compromise in which the federal school-funding policy allows for portability of money only if doing so will reduce what research suggests is one of the biggest impediments to equal educational opportunity: deep levels of economic segregation in American schools. A policy change that takes this reality into consideration could have a significant positive impact on the lives of millions of children.

Title I represents the largest funding stream in No Child Left Behind, the most recent iteration of the 50-year-old Elementary and Secondary Education Act. In 2014, the federal government distributed $14 billion of Title I money  among low-income students through a number of formulas. The biggest chunk of Title I money typically goes toward basic grants, providing funds to school districts based on the number of low-income children those districts serve. Other formulas within Title I provide extra funds to schools that have concentrations of poverty. The bonus in funding for high-poverty schools is based on research finding that, while it is a disadvantage to be poor, there is a second disadvantaged piled on top of that for students who go to schools where large number of their classmates are also poor.

Republicans in both the House and Senate have proposed changing the funding formulas so that low-income students would receive portable basic grants that they could take to their schools of choice, whether traditional public schools or charter schools. Some Republicans want to extend the portability options further so that they could be used in private schools, although most expect that idea to be voted down. The rationale for portability is that it will create a marketplace of schools in which high performers will be rewarded and low performers driven out of business. Some conservatives, like Rick Hess of the American Enterprise Institute, argue that current efforts to target funding at high-poverty school districts often fail to produce positive outcomes.

Democrats generally oppose portability to private schools because it would siphon funds from public education. But most Democrats also oppose portability within the public system because the targeted element of funding for concentrated poverty would be lost. A recent report for the liberal Center for American Progress argues that under a portability proposal backed by Republican Sen. Lamar Alexander, who chairs the Committee on Health, Education, Labor and Pensions, poor schools and districts would lose hundreds of millions of dollars. Targeting funds to schools with concentrated poverty makes great sense, they argue, because it is well established that "socioeconomic isolation has a devastating impact on student learning and achievement outcomes."

The center’s report is correct to suggest that, because Alexander’s proposal effectively eliminates targeted grants to high-poverty schools, it is regressive and wrongheaded. But the report’s recognition that socioeconomic segregation has "a devastating impact" raises a different question: Can Title I funding be restructured to reduce socioeconomic isolation itself? That is, rather than just giving extra money to high-poverty schools, why not go to the source of the problem and reduce the prevalence of high-poverty schools altogether?

Research from Montgomery County, Maryland, and elsewhere suggests that reducing socioeconomic isolation is a far more effective—and cheaper—way of improving academic achievement than spending extra money on high-poverty schools. In a 2010 Century Foundation report, Heather Schwartz, a researcher at the RAND Corporation, compared the effect of two separate programs in Montgomery County. Montgomery’s school-based program, following the traditional Title I logic, provided extra money—approximately $2,000 per pupil—to students in high-poverty schools that was aimed at reducing class sizes in the early grades, expanding professional-development opportunities for teachers, and establishing extended learning time. The second program, an inclusionary-zoning housing policy, allowed low-income families to live in public housing in middle-class neighborhoods and send their children to low-poverty schools.

Because families were randomly assigned to public-housing units throughout the county, Schwartz was able to fairly compare which students performed better over time: those in higher-poverty schools that received extra funding, or those in lower-poverty schools receiving lower levels of funding. Schwartz tracked students and found that those randomly assigned to middle-class neighborhoods and schools performed far better, cutting the math achievement gap with middle-class students in half. Being allowed to attend middle-class schools—where national research suggests that, on average, students are more academically engaged, parents are more involved in school affairs, and teachers have higher expectations—trumped the Title I approach. In other words, the extra funding doesn’t necessarily compensate for the disadvantages of attending high-poverty schools.

Those findings would suggest that the Republicans’ principle of portability, in fact, has in it the seeds of a solution to reduce economic segregation through public-school choice—if, and only if, portability is properly structured. In order to accomplish this, portable federal Title I funding, as well as state and local funding, would need to be weighted heavily enough to give poor kids sufficient money in their "backpacks" that middle-class public schools would want to recruit them to attend.

As it’s currently designed, the Alexander proposal is unlikely to provide that incentive. As former Obama education department official Peter Cunningham recently noted, "the amount of money that would follow an individual child is in the low hundreds." Educators know that it costs substantially more, on average, to bring low-income students into high levels of proficiency. That means that accepting low-income student transfers who come with only a marginal amount of extra money attached to them would likely reduce a school’s test scores and increase the chances of the school being labeled as "failing."

But every school has his price. What is the magical amount of extra money low-income students should have in their backpacks to be attractive to middle-class schools? That’s an empirical question that surveys of school administrators could answer definitively. Meanwhile, past experience shows that financial arrangements can be made to assuage middle-class schools. In St. Louis, Missouri, for example, a long-standing inter-district public-school choice program has allowed urban African-American students to transfer to suburban schools. In a 2010 paper for the Century Foundation, researcher Marco Basile noted that middle-class white suburban legislators supported this voluntary cross-district integration program because the money flows to the suburbs. The state also set aside some financial aid for St. Louis schools to offset the loss of funding to its urban campuses.

Is a grand bargain that weights funding toward low-income students and allows money to travel with children politically feasible at the federal level? There is some reason to think so. About a decade ago, the Fordham Institute, a right-leaning think tank, assembled a bipartisan group of public officials—from George W. Bush Education Secretary Rod Paige to former Bill Clinton Chief of Staff John Podesta—to endorse a program that would’ve provided extra funds to low-income students and then allowed that money to follow the child to a public school of choice. Congress is even more polarized today, but it’s notable that, on the reauthorization of the Elementary and Secondary Education Act, Alexander is working with Democratic Sen. Patty Murray to put together bipartisan legislation.

The principle that the federal government should play a special role in promoting genuine equal opportunity for low-income students remains as important today as it was when that law was first passed five decades ago. But there is also a half century of accumulated research to suggest that one of the best things the country can do for low-income children is give them a chance to attend a mixed-income school. The Republican effort to introduce choice and portability—if properly modified to create an incentive for socioeconomic school integration—could make the law more effective than it has ever been.