U.S. presidents don’t always pick the right person to be their No. 2. In fact, in the early days of the republic, presidents didn’t even choose their vice presidents due to a constitutional quirk that was quickly amended.

Here’s a list of three strange pairings in American political history—and a fourth that nearly happened.

The U.S. Constitution originally called for the candidate who received the second-most votes in the Electoral College to serve as the vice president to the Electoral College winner. Each elector cast two votes, and in the nation’s first election, in 1789, George Washington was unanimously elected president, with 69 votes, and John Adams got the No. 2 spot with 34 votes.

Adams had angled for the vice presidency with the hope of using it as a springboard for the presidency. When Washington announced he wouldn’t seek a third term—setting a precedent for future presidents—Adams ran for president in 1796 as the Federalist candidate. He narrowly defeated the country’s first secretary of state, Democratic-Republican candidate Thomas Jefferson, 71-68, putting these two ambitious politicians in the awkward roles of president and vice president.

Once friends (and fellow Founding Fathers), they had split over the direction of the country during Washington’s presidency. Adams believed in a strong central government, while Jefferson favored more states’ rights.

In the nasty race of 1800, Jefferson unseated President Adams, although the House of Representatives had to settle an Electoral College tie between Jefferson and Aaron Burr, who became the vice president.

That election helped lead to the 12th Amendment, which called for electors to cast separate ballots for president and vice president—avoiding repeats of vice presidents serving under their political rivals. Meanwhile, Adams and Jefferson eventually rekindled their friendship, and died on the same day—July 4, 1826, the 50th anniversary of the Declaration of Independence that both men had signed.

Abraham Lincoln and Andrew Johnson served together for less than two months, but Lincoln’s decision to make Johnson his running mate in the 1864 election—in the place of a loyal abolitionist vice president—proved to be one of the most consequential VP selections in U.S. history.

Lincoln’s original vice president was Hannibal Hamlin, a former governor and U.S. senator from Maine. In 1860, the nascent Republican Party chose him as Lincoln’s running mate because he provided geographic balance to the ticket (Lincoln was from Illinois). Hamlin’s strong opposition to slavery also made him an attractive vice-presidential candidate.

But in the leadup to the 1864 election, with the Union faring poorly in the Civil War, Lincoln decided to drop Hamlin in favor of Johnson, a former U.S. senator from Tennessee. When that state seceded from the Union, he had remained in the Senate, which won him plaudits in the North, while the South considered him a traitor. Lincoln made him military governor of Tennessee in 1862.

Two years later, the Republicans were anticipating unifying the country after the war, and they rebranded as the National Union Party for the 1864 election. Putting a Democrat from a southern state on the ticket was seen as a way of helping that unification.

Lincoln was assassinated in April 1865, and Johnson was sworn in as the new president, after serving as vice president for only six weeks. The new president proved to be an obstacle to helping newly freed Black citizens gain their rights.

“Republicans had hoped that as the military governor of Tennessee who had dealt harshly with slaveholders, Johnson would prod fellow southerners to accept the new order,” wrote Jules Witcover, author of the book The American Vice Presidency: From Irrelevance to Power, in a 2015 Politico article. “Instead, he bent over backward to help them restore much of what had been the social and cultural mores of the Old South.”

Johnson opposed the 14th amendment, which granted citizenship to all people born or naturalized in the United States—including formerly enslaved African Americans. He would be the first president impeached, and came within one vote being convicted in the Senate.

In 1932, Franklin D. Roosevelt, the Democratic governor of New York, also sought to have balance on his ticket by tapping House Speaker John Nance Garner, a conservative Democrat from Texas, as his running mate. After FDR defeated Herbert Hoover in a landslide, Garner helped lobby for the president’s New Deal legislation among his former colleagues in the House. But as an anti-labor conservative, he eventually became disenchanted with FDR’s liberal legislative agenda, such as the Social Security Act.

Garner also quickly had second thoughts about taking the job in the first place, complaining he was just “a spare tire of the government” under Roosevelt. “Worst damn-fool mistake I ever made was letting myself get elected vice president of the United States,” he said after leaving office. “Should have stuck with my old chores as speaker of the House. I gave up the second-most important job in the government for one that didn’t amount to a hill of beans.” He also famously declared, “The vice presidency is not worth a bucket of warm piss.”

Garner was angry when FDR mounted a bid for a third term in 1940, and the sitting vice president made the remarkable decision to run against his own sitting president for the Democratic nomination. But Roosevelt easily dispatched him, and, not surprisingly, ditched him as his running mate, replacing him with the liberal Henry A. Wallace. Four years later, Harry Truman replaced Wallace on the ticket, and ascended to the presidency following FDR’s death in 1945.

A dozen years before he crushed Hoover, FDR floated the idea of joining him on a national ticket, with Hoover at the top. Both men had served in the administration of Democratic President Woodrow Wilson—Roosevelt as assistant secretary of the Navy, and Hoover as head of the newly-created U.S. Food Administration, which oversaw the nation’s food supply during World War I.

Like Dwight D. Eisenhower a generation later, Hoover was a popular national figure with no publicly declared party affiliation, and both Republicans and Democrats eyed him as a potential nominee in 1920. He had earned the admiration of many for his wartime relief efforts, getting food to civilians caught behind enemy lines in Belgium and France.

“There was a strong sense that Americans were ‘weary’ of the familiar Republican and Democratic politicians and that Hoover, a ‘practical man’ of ‘straightforward accomplishments,’ represented something fresh,” writes Kenneth Whyte in his 2017 book, Hoover: An Extraordinary Life in Extraordinary Times.

Meanwhile, FDR, just 38, sought to become his party’s vice-presidential nominee—a path that his cousin, Republican Teddy Roosevelt, had used to ascend to the White House about 20 years earlier. When a politically connected Harvard classmate, Louis B. Wehle, told FDR he had discussed with party leaders how a Hoover-FDR ticket could win that fall, Roosevelt gave him the green light, Jean Edward Smith writes in the 2008 biography, FDR. Once again, geographic balance was a factor. FDR was from New York, while Hoover was from California.

“Hoover is certainly a wonder,” FDR told Wehle, according to Smith’s book. “I wish we could make him President of the United States. There could not be a better one. … You can go to it as far as I’m concerned. Good luck.” The New York Times reported a dozen years later that “friends of the two men labored seriously for a Hoover-Roosevelt ticket as a ‘liberal’ slate that might bring victory.”

On March 6, 1920, FDR and his wife Eleanor dined with Hoover but “could not smoke him out” about his party allegiance, Smith writes. Finally, at the end of March, Hoover announced he was a Republican and would be willing to accept the GOP’s nomination for president. But his association with Wilson and his public call in 1918 for voters to keep Congress in Democrats’ control helped sink his support with some Republicans on Capitol Hill.

In the end, the GOP nominated Warren Harding, and FDR got the VP nod on the Democratic ticket, under presidential nominee James M. Cox. Harding won in a landslide, and Democrats wouldn’t regain the White House until FDR’s own landslide victory in 1932.