Now that her nomination is assured, Hillary Clinton is stepping up her search for a running mate, and though she has said only that she’s considering “the most qualified people,” the speculation of whose name will go on bumper stickers and T-shirts has centered largely on a small number of leading Democrats.

There is of course Clinton’s rival, U.S. Sen. Bernie Sanders of Vermont, who could balance Clinton’s reputation as a friend of Wall Street and supporter of free trade pacts. But if he were picked, his comments in April that Clinton isn’t “qualified” to be president, among other slashing attacks, would be fodder for the Republicans who would most assuredly repeat his words like a drumbeat all the way to November.

So Sanders is probably out.

Another oft-cited potential running mate is Ohio Sen. Sherrod Brown. In many ways he’s an ideal pick with a reputation as a populist liberal defender of the blue-collar workers who are watching their jobs go abroad and their paychecks shrink. Brown could be an effective attack dog against Team Trump, and might be able to deny Ohio to the GOP nominee. In modern times, no Republican has won the White House without winning Ohio.

But there’s one problem with Brown. He would vacate an important seat in the Senate at a time when the Democrats are trying to regain control, and Republican Gov. John Kasich would appoint his successor. He might be in the running, but it could be a risky bet.

Then there’s Massachusetts Sen. Elizabeth Warren. She shares many of Sanders’ views but has kept her criticisms of Clinton at bay. Would a two-white-women ticket play better in the election than, say, a Clinton and a Hispanic running mate? 

“I am looking at the most qualified people, and that includes women, of course,” Clinton told CNN’s Anderson Cooper on Tuesday. So consider Warren a potential running mate.

Here are some other possibilities:

Minnesota Sen. Amy Klobuchar – Minnesota’s Rising Star

There are several women who have been name-dropped by pundits, including former Homeland Security Secretary and Arizona Gov. Janet Napolitano and California Attorney General Kamala Harris, who is running for the Senate. Klobuchar is a rising popular star in a state where Democrats would likely win a special election to replace her. She shares many of Clinton’s views on healthcare policy and was rumored to be considered to replace President Barack Obama’s Attorney General Eric Holder in 2014. That she’s from a “flyover state” helps blunt Clinton’s coastal elitist reputation.

Labor Secretary Tom Perez – The Wage-Hike Warrior

Perez would be an ideal candidate on two counts: He’s a high-ranking Obama administration official who steered his department toward joining the movement to boost wages for the working poor, boosting his progressive cred, and he’s of Dominican descent. Having the first female president with a Hispanic running mate who advocates for higher wages for the lowest-paid would likely play well among nonwhite voters.

Virginia Sen. Tim Kaine – The White Southerner

An establishment Democrat with an enticing background – a Spanish-speaking former Christian missionary from a swing state – Kaine was the first high-ranking elected official to endorse Clinton, in May 2014. He has served as head of the Democratic National Committee. If Clinton decides to avoid picking someone to her left, Kaine could be a way to lure moderate Southern Republicans already poised to vote ABT – Anybody But Trump.  

HUD Secretary Julian Castro – The “Good” Guy

When asked whether she’s considering the Housing and Urban Development secretary as a running mate back in October during a rally in San Antonio, Clinton replied:  "I am going to look really hard at him for anything, because that's how good he is.” That alone makes Castro, previously mayor of San Antonio, a candidate for the list. Like Perez, he has Hispanic roots. Unlike Perez, those roots are in Texas, with Mexican heritage. And he's a defender of LGBT rights.