Stonehill, in Massachusetts, had the biggest jump in Pell students, by focusing on candidates within 50 miles of campus and increasing financial aid. “It enhances the education of all students to meet people who are different than they are,” Eileen O’Leary, a Stonehill administrator, said.

Of course, the overall stagnation in the numbers means that for almost every college that’s becoming more diverse, another college is becoming less so. The share of Pell recipients at Duke, Harvard, Rice, Williams and even most University of California campuses has fallen somewhat since 2011.

Most low-income students who attend top colleges thrive. Merely going to college isn’t enough to change a teenager’s life. The benefits of college – higher income, better health, greater life satisfaction – generally depend on graduating, research shows. Which is one reason you sometimes hear worries about whether low-income students can fit in at top colleges.

But the evidence suggests that they can and do.

The median six-year graduation rate for Pell students at the colleges in our index is 84 percent, only slightly lower than the overall rate of 85 percent. College certainly involves challenges for many low-income students, but they largely meet them when they attend a top college. That’s a big reason these colleges matter: They don’t leave many students saddled with the toxic combination of debt and no degree.

On some campuses, the Pell graduation rate even exceeds the overall rate. One of them is the University of California at Irvine.

Irvine’s story is fascinating. It owes its existence to California’s population explosion after World War II, which created a quandary for the state’s public universities. Either they had to step back from their historic mission – and educate a much smaller share of California teenagers – or they had to grow enormously.