Free college sounds like a great idea, when you first hear the words. That might be why Bernie Sanders was able to whip up so much enthusiasm around the idea in his 2016 U.S. presidential bid, and is still campaigning for it to this day. For anyone who has had to pay sky-high tuition at a big-name university, or dealt with the crushing weight of student loans, those two magical words must seem like a rope being thrown down from heaven.

But the dream of free college is a mirage. While much needs to be done to fix the United States’ overpriced university system and deliver the bounties of higher education to more people, plans like Sanders’s — which would eliminate tuition at all public universities — are not the way to do it.

One problem, which many others have pointed out, is that free college would disproportionately benefit the wealthy and upper-middle class. An analysis by researcher Matthew Chingos for the Brookings Institution found that students from higher-income families tend to go to schools where tuition is higher, whereas students from more disadvantaged backgrounds tend to go to cheaper in-state schools and community colleges.

Of course, this might change if all public colleges were free, since high tuition is one of the reasons why so many kids from lower-income households don’t go to expensive schools. But there are reasons to think it wouldn’t. Prestigious colleges that spend a lot on renowned professors, fancy dormitories and the like would still have an incentive to admit lots of kids from rich families, because these kids are more likely to get rich themselves, and therefore to make large alumni donations. Tuition, after all, accounts for only about one-fifth of public university revenue. Also, rich kids tend to have better grades and test scores, so prestigious public universities will admit more of them in order to maintain their status.

So free college would yield a lot of benefits for the rich, while failing to pay the non-tuition costs — such as room and board, textbooks and meals — that are a big burden for poorer students.

Another problem with free college is that it would probably worsen the quality of universities. If the government paid for all tuition, it would have to cap the price, to avoid having government expenditures spiral out of control. Some of the price cap could be accomplished by cutting the number and the salaries of administrators. But some would undoubtedly come at the expense of hiring good professors, who can command high salaries in the private sector. And some would come from limiting spending on dormitories and other student facilities, as well as the world-class scientific research that makes U.S. universities the best in the world.

That drop in quality would reduce the benefits that accrue to poor and working-class kids from attending formerly elite public universities. Top professors would leave public schools for better pay at private ones (or for the private sector), and top students would follow. The public university system would become more like the U.S. K-12 public school system — free and universal, but not a very powerful a tool for equalizing opportunity. Ultimately, lower-income kids might not even find it worth their while to go to these colleges, opting instead to enter the workforce and earning at least a modest sum of money right out of high school.

There is evidence to support this outcome. England, which used to provide tuition-free public universities, switched to a tuition system in 1998, and has raised fees several times since then. Economists Gill Wyness, Richard Murphy and Judith Scott-Clayton studied the impact of getting rid of free college. What they found might prove a shock to Sanders supporters:

“The analysis shows that since the move from a free higher education system to a high-fee, high-aid system, university enrolment has increased substantially, with students from the poorest backgrounds experiencing the fastest increases in participation. Moreover, university funding per head has recovered dramatically since the introduction of fees.”

England’s experience shows that there is a much better way to provide low-income students with the opportunity to get a cheap high-quality education. Instead of making college free for all, England focused on providing help to disadvantaged students.

One way it did this was through means-tested grants — a system of need-based financial aid similar to that used by elite private universities like Stanford and Harvard in the U.S. The second policy was income-contingent loans — debt that students would only have to pay back if they succeeded in their careers.

In other words, instead of having the government subsidize the rich — as Sanders’s plan would do — England had both rich kids and government subsidize poor kids. And it worked.

The U.S. should copy England’s example. It should also build more public schools, to expand the number of kids equipped to get high-quality secondary education. Free college might make a good campaign slogan, but there are much better policies out there.

Noah Smith, a former assistant professor of finance at Stony Brook University, is a Bloomberg View columnist. He blogs at Noahpinion.