A new report released Wednesday by the U.S. Department of Education highlights what it says are effective strategies by colleges and universities to increase college access and to support successful outcomes for low-income students. But officials also stressed in a separate conference call that there’s still a lot of work to be done on this front.

Fulfilling the Promise, Serving the Need: Advancing College Opportunity for Low-Income Students highlights public and private institutions of higher education that enroll relatively high shares of students from low-income backgrounds who receive Pell Grants, and who graduate at relatively close to the same rates as all students. The report also looks at colleges whose Pell Grant recipients earn at least $25,000 annually six years after enrolling.

Here’s a chart from the report highlighting those statistics for certain four-year public institutions of higher education—the Education Department says these are examples of good outcomes for students:

The report also highlights efforts by President Barack Obama’s administration to increase the pathways for students from low-income backgrounds to attend college, from increasing Pell Grant funding to expanding tuition tax credits and establishing more manageable methods of repaying student loans.

In addition, the report highlights the administration’s “First in the World” initiative that focuses on strategies to improve outcomes for students in higher education (particularly for students from low-income backgrounds) at places such as Georgia State University, Spelman College, and the University of Southern California.

But on a conference call with reporters to discuss the report, Secretary of Education John B. King Jr. said that too many barriers remain for low-income students seeking admission to colleges and universities, and that significant graduation rate gaps persist between Pell Grant recipients and students who don’t receive Pell Grants.

“Unfortunately, today, those success stories are the exception, and they ought to be the rule,” King said, adding that the success stories in the report aren’t the only ones for people to study.

The report states, for example, that among the most-selective higher education institutions as identified by a 2014 Barron’s report, only 3 percent of students come from the bottom-income quartile.

Roberto Rodriguez, the deputy assistant to Obama for education, told reporters that the administration doesn’t want to call out specific institutions that are falling short, but instead thinks highlighting successful strategies and publicizing colleges and universities that have done well will make a major difference.

Asked how the issue of college affordability can be addressed aside from increasing direct student aid, Undersecretary for Education Ted Mitchell also highlighted instances where colleges and universities have either frozen or reduced tuition costs.

“We understand from those institutions that it’s been an important driver of enrollment,” Mitchell said.

Read the full report.