This story appears in the May 2016 issue of Playboy. Subscribe

Cloistered in a brick colonial house off Embassy Row in Washington, D.C. and high atop Trump Tower in Manhattan, the presumptive presidential nominees are now struggling with the first momentous decision voters will see them make: the selection of a running mate.

As Hillary Clinton and Donald Trump continue to fight for delegates in the remaining primaries, behind the scenes their campaigns have transitioned to a new, secret phase that will reveal what kind of president they might be. In 1976, when a one-term governor from Georgia named Jimmy Carter landed the Democratic nomination, he was unknown to most of the country. But he chose a respected U.S. senator, Walter F. Mondale of Minnesota, as his running mate. “It sent a powerful message that Carter was going to make sound, sensible decisions,” says longtime Democratic strategist Bill Carrick, who has worked in two veep-selection cycles.

Carrick and others who have been integral to similar operations sketch out scenarios in which the leading candidates will hunker down with a tiny core of lawyers, public relations specialists and even private investigators, all of them tasked with finding the “right” individual to serve as VP. They will vacuum every detail of a candidate’s life, from bank balances to anyone they may be schtupping, to make sure there are no secrets that could derail the campaign.

In 2000, the man George W. Bush tasked with leading the search for Republicans, Dick Cheney, selected himself. Four years ago, when Mitt Romney challenged President Barack Obama, he cast a wide net with his Project Goldfish, named for his staffers’ affinity for the snack crackers. Romney started with 24 candidates and worked his way down to the finalists, who were given code names; Governor Chris Christie of New Jersey was known as Pufferfish. (Romney had a fondness for making fun of overweight people, as reported by John Heilemann and Mark Halperin. When he saw an obese woman he would joke to male aides, “There’s your date for tonight.”) Romney kept his files locked in waterproof safes inside offices that required PINs to enter.

This process should be familiar to Clinton. In 1992, when Bill was running for president, he even vetted himself by hiring private detective Jack Palladino to get a jump on the women with whom Bill had had affairs in case they caused him trouble down the line—the “bimbo eruptions,” as they were known in the Clinton campaign. Hillary’s operation is probably more high-toned, with lawyers from the D.C. firm Williams & Connolly reviewing dossiers of candidates who have been poll-tested and focus-grouped.

Trump should know how to hire a number two after starring on The Apprentice for 14 seasons. Trump’s friend Roger Stone, the Republican consultant who exposed New York governor Eliot Spitzer’s penchant for prostitutes, insists that the billionaire’s approach to finding a veep will be unorthodox. “Nothing’s in and nothing’s out,” Stone says. “People think Trump is Machiavellian, but he’s really not. He’s flying totally by the seat of his pants.”

Even with that, the presidential nominees will ask whether a prospective veep can deliver votes. In 1960, Democrat John F. Kennedy of Massachusetts picked Senate Majority Leader Lyndon B. Johnson of Texas because Johnson was a national figure with a powerful political machine. But there’s no one with LBJ’s sway on the scene today, so the idea of a veep pick who can deliver a state as Johnson did is fantasy. Romney’s advisors believed that by selecting Paul D. Ryan (now Speaker of the House), they had a chance to turn Wisconsin Republican. But Obama won 53 percent of the vote there. Ryan couldn’t even carry his home county, where he was clobbered by almost 25 points.

“So the nominee ends up saying, ‘Maybe I should just figure out what kind of vice president someone might be and how much help they could be in the White House,’ ” explains Carrick. Or, to paraphrase Richard Nixon, nobody can help you. Just find someone who won’t hurt you.

Smart nominees will use their veep selection to compensate for their own weaknesses. For Clinton that means finding someone who will blunt her association with business-as-usual Washington and Wall Street. She also needs someone who will galvanize millennials as Bernie Sanders has. “That’s the big chunk of the Obama coalition that she desperately wants,” Carrick says.

Trump has to decide whether he wants to try to make nice with those in the party who loathe him for his opposition to interventionist wars, open borders and globalism—staples of Bush Republicanism and the neoconservative faction. Trump’s stated plan is to get a veep with deep political experience. In that vein, a strong choice would be a governor from a big swing state, such as Rick Scott of Florida or Trump’s opponent for the GOP nomination John Kasich of Ohio. Then he’ll pray that the state swings Trump’s way. “But if he picks Kasich,” says Stone, “Trump would need a food taster…and yes, that was on the record.”