School choice can be more than just a “lifeboat” for students needing to escape troubled public schools. When structured correctly, school choice can create competition among both private and public schools to improve their performance.

That, say Jay Greene and Ryan Marsh, is what’s going on in Milwaukee right now. Milwaukee has one of the nation’s largest and longest-running school choice programs. Green, the head of the University of Arkansas’s Department of Education Reform, and Marsh, a graduate student at Northwestern University, did a study recently to see if the existence of school choice induces public schools to perform better in order to discourage students from leaving. They found that, indeed, the more voucher options that students in public schools have, the better they fare academically. School choice, in other words, can help students who stay in public schools, too.

That’s how competition is supposed to work, and, indeed, it’s a major part of the theory behind why school choice should work. Yet critics of Milwaukee’s program have been harping for years on the fact that previous studies have found little difference in academic achievement between students in choice programs and students in public schools. But if schools are competing, then it shouldn’t matter that much whether they are nominally private or public schools.

The idea that it is competition, rather than private management of schools per se, that is valuable has sometimes been lost in the design of school choice programs. For instance, in the District of Columbia, the D.C. Opportunity Scholarship program is now showing results for the kids in the program. Late last week, the Department of Education released a study showing that students in the voucher program for three years achieve a higher reading level than their public school counterparts. That’s good news for the program, but there is no competition created by that success because participation in the program is capped. D.C. public schools don’t have to worry about losing additional students—or money—to the choice program.

The D.C. program is slated for termination next year unless Congress acts to reauthorize it. Given the evidence that school choice works, lawmakers should consider not only reauthorizing the program, but also creating true competition in education by lifting the caps and letting the money follow the students to whatever schools they choose.