So far, nearly every U.S. Secretary of Education came into the job with a long record in K-12 policy. But, if Hillary Clinton is elected president, she may break with that longstanding tradition.

No, you didn’t miss an announcement from the Clinton campaign, which is busy trying to win the election, not pick its cabinet.

But there are a lot more names of college presidents or university system leaders in the rumor mill on the Democratic side than there have been in past years. (More on just who later down.)

That’s partly because Clinton has spent way more of her time on the campaign trail talking about higher education access and affordability, which was a signature issue for her rival for the Democratic nomination, Sen. Bernie Sanders of Vermont.

Clinton even revamped her college-cost proposal to better match Sanders’ pitch. Her plan would offer free tuition at public universities for students from families that make less than $125,000 a year. (Everything you ever wanted to know about Clinton’s education proposals and how they compare to GOP nominee Donald Trump’s here.)

Clinton’s proposal would amount to a “very expensive operation,” said Marshall “Mike” Smith, who has served in the department under three different presidents, including as acting deputy secretary under President Bill Clinton. “It might be easier for a well-known college president to carry the load on that in Congress.”

There are plenty of political vehicles for a new higher education proposal. Reauthorizations of the Higher Education Act and the Carl D. Perkins Career and Technical Education program are still pending, while congressional lawmakers passed the Every Student Succeeds Act last year and probably won’t engage on K-12 in a big way for a while.

Plus, there’s “a need for a good solid debate about the purpose of postsecondary education, the cost of postsecondary education,” said Jack Jennings, who served as an aide to Democrats on Capitol Hill for nearly three decades. A secretary with a postsecondary background could help lead that debate, he said.

What’s more, ESSA sought to rein in the secretary of education when it comes to a lot of the flashier K-12 issues, including teacher evaluations, standards, turnarounds, and more. But the secretary still has as much running room as ever when it comes to higher education.

“The decision has been made in elementary and secondary that the feds will not take much of a role for a while,” Jennings said. “It would be prudent for the federal government to step back a little and let states and school districts go ahead and do what they can.”

And, not insignificantly, there a lot of issues in K-12 that tend to divide Democrats, including charter schools, testing, and teacher evaluation. Higher education access, though, is a lot less politically dicey. It could be pretty easy to get much of the education community behind a postsecondary pick who doesn’t have much of track record in K-12.

Still, a secretary from the higher education world could result in a bigger role on K-12 for other high-level folks at the department (the deputy secretary, the undersecretary, the assistant secretaries of planning, evaluation, and policy, or the assistant secretary of elementary and secondary education).

And it would be a significant departure from past picks. The last four secretaries—Rod Paige, Margaret Spellings, Arne Duncan, and John B. King Jr.—all had big K-12 backgrounds. (Paige and Duncan were district superintendents, of Houston and Chicago, respectively. King was the state chief in New York, and Spellings had been a top White House adviser on K-12 issues. She also advised President George W. Bush on K-12 when he was governor of Texas.)

And the two secretaries before that were governors who had been very active on K-12 issues. (Richard Riley of South Carolina served under President Bill Clinton, and Lamar Alexander of Tennessee served under President George H.W. Bush.) In fact, you have to go all the way back to Lauro F. Cavazos, the former president of Texas Tech University, who served in both the Reagan and first Bush administrations, to find a secretary who came from the higher education world.

So would a secretary from higher education mean K-12 would be just an afterthought at the department? Don’t bet on it, Jennings said.

“You can’t ignore K-12,” he said. For instance, the next secretary and his or her team will have to turn pretty quick to approving—or rejecting—state’s ESSA plans, which are due as early as March or as late as next summer.

College Presidents to Watch

Some college presidents who folks have suggested might make a good secretary of education include: Mike Crow, the president of Arizona State University; Janet Napolitano, the president of the University of California system (and a former Secretary of Homeland Security, and governor of Arizona); Nancy Zimpher, the New York state higher education system chancellor; Eduardo Padron, the president of Miami Dade Community College; and Freeman A. Hrabowski III, the president of the University of Maryland, Baltimore County, who chaired President Barack Obama’s Advisory Commission on Educational Excellence for African Americans.

To be sure, there are still plenty of K-12 names in the mix. Many folks are guessing that if elected Clinton could go the same route her husband did with Riley and pick a current or former governor (Gov. Jack Markell of Delaware, former Gov. Howard Dean of Vermont, Gov. John Hickenlooper of Colorado, former Gov. Jennifer Granholm of Michigan, and more.)

And others are betting she’d choose someone else from the K-12 world, like Denise Juneau, who is running for Congress and is currently Montana’s state superintendent, or Kaya Henderson, the former District of Columbia public schools chancellor. (Henderson’s has said she’s not interested in the gig.) More here.

Would Trump, if elected, also pick someone from the higher education world? It’s tough to say. Trump has been a lot more vocal on school choice than on any other education issue. Presumably his secretary would share his views on that. A Trump advisor, Sam Clovis, said he wants student loans to originate with banks, not the federal government. More here.