There is a powerful case for giving every possible advantage to better-behaved poor kids who are fortunate enough to have caring parents. School vouchers offer them an escape route from troublesome and unmotivated peers, negative peer influences and anarchic environments where teachers have to spend much of their time trying to maintain order. But it also means that school vouchers alone won't solve the problem of poor kids and lousy schools. Vouchers may just concentrate the problem further.

Almost a decade ago, New Zealand embarked on the closest thing we've seen to a national school-voucher experiment. Parents were given the right to choose the school their kids attended. This gave schools that attracted more applicants than they could accommodate great discretion over whom they accepted. The result: The best schools became even better, as they attracted the highest achievers. But the worst schools grew worse—with evergreater concentrations of difficult-to-teach students from impoverished homes. Vouchers—with nothing more–led to economic and social polarization.

But polarization already exists in the U.S. because of residential segregation by income, as well as the stark relationship between a community's tax base and the quality of its schools. Poor kids are more likely to attend underfunded schools than kids who aren't poor. Analysis from the National Center for Education Statistics shows that most poor students live in districts that spend less per student than their state's average. The Department of Education recently reported that much of the teaching in America's poorest schools is being done by teacher's aides without college degrees, rather than by qualified teachers.

The only way to begin to decouple poor kids from lousy schools is to give poor kids additional resources, along with vouchers enabling them and their parents to choose how to use them. Per-pupil public expenditures now average between $6,000 and $7,000 a year in the U.S. (with some states spending as much as $9,000, and others-as little as $4,000). Ideally, a child from America's poorest 20% of families would receive a voucher worth between $10,000 and $12,000. Children from families in the next quintile would receive vouchers worth between $8,000 and $10,000. The vouchers could be used at any school that meets certain minimum standards, regardless of whether the school is now dubbed "public," "charter" or "private." (Leave aside, for now, the tricky First Amendment issue of public money for religious schools.)

What would be the likely result of such progressive vouchers? Schools already in easy geographic reach of poor kids would get an immediate infusion of billions of dollars they could use to upgrade physical plants, buy new textbooks, initiate afterschool programs, and hire more and better teachers. But they would also have to compete with other schools nearby which thought they could put those sizable vouchers to even better educational use.

Even some suburban schools can be expected to enter the competition. The large vouchers would make it worthwhile to send vans to pick up and drop off groups of inner-city students. Although the most intensive competition would center on the best-behaved poor kids whose parents were most aggressive in seeking out good schools, the large vouchers would spur schools to recruit and retain more difficult children as well. Students, parents, and the schools they select would sign contracts for a minimum of two years, outlining their mutual objectives and responsibilities for meeting them.

Wealthier suburban schools would have even greater incentive to compete for students from poor families if the progressive voucher extended all the way up the income ladder. If children from families in the top 20% of income got vouchers of, say, $2,000 to $4,000 a year, schools in wealthier communities would make every effort to seek out enough $10,000 or $12,000 "vouchered" students in their region to meet their budgets.

The Challenge

Do you like the idea? Don't hold your breath. A progressive voucher system is a very long shot for now. For it to become a reality, we would need a substantial over haul of the financing of public education. This would entail pooling local property taxes from both rich and poor communities (which the rich are likely to resist with no less intensity than they've opposed state schemes to better equalize educational spending) and dramatically increasing federal and state funding.

Teachers' unions may not look fondly upon the idea either, although it could result in higher salaries for good teachers. The largest challenge is to convince each side in the current education battle that they have only part of the answer, and their opponents have the other.

Mr. Reich, former secretary of labor, is professor of social and economic policy at Brandeis University. His next book, "The Future of Success," will be published in January by Alfred A. Knopf.