Every year countless high-achieving students from disadvantaged families flock to colleges that others might call their “safety schools.” The good news—they’ve reached college. The bad news—they are heading off to less-selective institutions than they are qualified to attend. The really bad news—that may increase the odds they will drop out.

The reality is that the college-recruitment and -application processes for low-income students are like a middle-school dance—both colleges and students are holding up the walls, curiously staring at each other across the expanse of gym floor. Up to now, researchers, advocates, and reformers have paid most of their attention to the students’ side of the dance floor, where even the most gifted low-income students and their families often lack information about where they are eligible to attend or how much it will cost them. Scared by high sticker prices, they don’t realize how financial aid would reduce the fare. The College Board, for example, recently announced it would send information about select colleges to low-income seniors who score in the top 15 percent on the SAT or PSAT.

But the scrutiny should not fall on only the students and their counselors. In the rush to ensure that students are adequately prepared and informed to apply to the best colleges they can get into, we have paid less attention to an equally important variable: colleges’ appetite and capacity to enroll low-income students.

While President Obama’s recent proposals to make college more affordable try to nudge institutions to enroll more Pell Grant recipients by providing bonuses and including the percentage of such recipients in a new college-rating system, it is too soon to tell whether they could shape the behavior of many selective colleges. Arguably, the impact (if the plan were even to be put into effect) might be more like herding cats, as institutions perched atop other college-ranking lists would have little incentive to court low-income students— even though they have deep enough pockets to do so.

The data are discouraging, as they show that many colleges aren’t actually looking to find dance partners. In the past decade, most selective colleges have sparingly created new freshman seats, while enjoying mounting numbers of applicants. At the same time, many of those colleges have opened their doors only a crack to let in a modest increase of low-income students.

The University of Virginia is the latest college to bail on low-income students, in essence telling underprivileged applicants to look but not touch. Citing mounting program costs, UVa recently announced it was cutting back on its highly lauded AccessUVa financial-aid program, which had ensured low-income students’ financial needs would be met with grants and not loans. One of the first of its kind at an elite public university, the program mirrored the Ivy League no-loan pledges and has been regarded as an example of institutional commitment to low-income students. Other public institutions are also reneging on promises to educate the poor, as they shift institutional aid to higher-education students. A recent analysis by ProPublica, published in The Chronicle, shows that, from 1996 through 2012, public colleges and universities gave fewer and smaller grants to students with the lowest family incomes.

Scaling back financial aid is only one of several institutional policies that dissuade low-income students from enrolling at particular colleges. For example, in recent years, some colleges have done away with need-blind admissions, increased merit aid, or re-instated early-decision programs, which have been widely criticized for disadvantaging low-income students who cannot commit to a college before knowing the financial-aid offer. Ask a seasoned high-school guidance counselor, and he or she can quickly tick off the colleges that “gap” their students’ financial-aid packages (i.e., do not meet the full amount of financial aid needed) or exhibit only half-hearted recruitment efforts. Such institutional policies perpetuate a bifurcated system, where only a small number of smart low-income students wind up at America’s most elite colleges, while the majority enroll in open-access institutions. With lower resources than their elite competitors, the latter often have lower rates of student success.

It should come as no surprise, then, that our higher-education system is becoming increasingly stratified by race and income. As a report from Georgetown University’s Center on Education and the Workforce demonstrated, over the past nearly 15 years, a larger proportion of high-income students have enjoyed the benefits of rich selective institutions, while low -income students, regardless of the academic ability, have been increasingly concentrated in poorer nonselective two-year and four-year colleges that have lower completion rates.  In fact, research on “undermatch” shows that the likelihood a low-income student enrolls in a college that matches his or her academic ability is close to chance.

Indeed, if colleges do not build capacity to accommodate the growing population of low-income students, it’s possible that  admissions offices at top colleges with applications from qualified low-income students will cut the chances that any one individual will get in or get a good financial-aid package.

While we can—and should—improve on the academic preparation and information students receive about college, we will not be able to move the needle on stubborn problems like rising inequality through guidance or better preparation alone. So long as the incentive to enroll low-income students is weak, many colleges will stay off the dance floor with policies and practices that keep down the number of low-income students on their campuses.

Awilda Rodriguez is a research fellow at the American Enterprise Institute.