(Note: An earlier version of this story was published without the final section. The section has been restored.)

It was clear, watching both Justin Trudeau and Emmanuel Macron shake hands for the first time with Donald Trump, that each had prepared for the moment.

Trump's notorious grip-and-drag-down handshake already had been widely analyzed as a display of dominance (as in his arm-wrenching grip with Supreme Court nominee Neil Gorsuch).

The French and Canadian leaders were determined to avoid playing the beta to Trump's alpha. (Macron managed it again during his recent visit to the White House, despite that weird dandruff-flicking gesture by Trump). Both have successfully evaded Trump's attempts to drag them under in public. But they do it in different ways.

"Body language experts" around the world praised Trudeau's deft handling of the Trump paw during his visit to the White House in February, 2017. It was "a master class in getting it right," Judi James told the U.K.'s Daily Express.

Coming to grips with Trump

"Trudeau disarmed Trump at their first meeting by getting in too close to fall victim to Trump's notorious power shake or shake-and-yank combos that were diminishing the status of other world leaders on their first visits to the White House. His canny arm-pat on the president's bicep suggested Trudeau was the one in control."

Prime Minister Justin Trudeau meets with U.S. President Donald Trump in the Oval Office of the White House in Washington, D.C. on Wednesday, Oct. 11, 2017. (Sean Kilpatrick/Canadian Press)

Macron also avoided being dominated during his first encounter with Trump in Brussels a year ago — but he did so by trying to dominate right back.

Here's what the pool report for the encounter said: "Each president gripped the other's hand with considerable intensity, their knuckles turning white and their jaws clenching and faces tightening."

"Trump seems to just want his hand back," another reporter in the room tweeted.

Macron was open about his approach with a reporter for the Journal du Dimanche: "My handshake with him, it's not innocent. It's not the alpha and the omega of politics, but a moment of truth."

The two approaches could almost serve as metaphors for how Macron and Trudeau have chosen separately to handle the world's most prominent bull in a china shop. Trudeau responds by "getting in too close" for the president to land any heavy blows, while Macron is more willing to go toe-to-toe and wrestle.

"I think Mr. Trudeau is a lot closer to Washington both metaphorically and physically, and that makes all the difference," said David Shribman, syndicated columnist and executive editor of the Pittsburgh Post-Gazette.

"Where you stand depends on where you sit. And Mr. Trudeau sits in Ottawa and not in Paris."

While France and the U.S. are important allies which frequently act in concert (as in the recent attack on Syria), they are not joined at the hip economically as the U.S. and Canada are.

French President Emmanuel Macron's trip to Washington marks the first state visit for the Trump White House. The two presidents may disagree on a number of key issues, but both leaders see the visit as an opportunity to strengthen their own political profiles. 2:04

There is no single overriding issue between the two countries to which all other issues take a back seat. In Canada, there is: the renegotiation of NAFTA.

The Trudeau government has applied its "sunny ways" doctrine to the whole relationship with the Trump administration in an obvious effort to avoid becoming the focus of Trump's ire.

That approach extends to letting slide even public provocations — like Trump's admission in March that he lied in a meeting with Trudeau about a U.S. trade deficit with Canada. Canadian officials react to such episodes with private bemusement and public silence.

Being 'good-looking' helps

Trump's public expressions of fondness for Trudeau ("my newfound friend ... a very good guy, good-looking") are similar to those he now expresses about Macron ("He is perfect").

Trump has often suggested that the physical appearances of men are as important to him as those of women in assessing their worth or suitability for high office.

During the presidential campaign, Trump famously suggested that Republican rival Carly Fiorina was not good-looking enough to get elected. "'Look at that face!" he said on live television. "Would anyone vote for that? Can you imagine that, the face of our next president?"

Recently, when stumping for Republican Rick Saccone in western Pennsylvania, he dissed the face of the conventionally-handsome Democrat candidate, Conor Lamb.

"I hear he is nice looking," Trump said. "I think I am better looking than him … Personally, I like Rick Saccone. I think he is handsome."

Macron a change agent

Macron has presented himself at home as something of a Trump whisperer. Even his domestic opponents were forced to admit he scored a coup when he invited Trump to the Bastille Day parade in Paris, where the two watched the flower of the French armed forces march up the Champs-Elysee.

Trump loved the parade. No sooner than he returned to Washington, he ordered a horrified Pentagon to look into organizing one for the U.S.

But if the two leaders both seek to manipulate the U.S. president's ego, the Canadian's ultimate objective is more limited than the Frenchman's. Trudeau seeks only to keep Trump from harming Canada, blowing up NAFTA, or deciding that Canada is a problem.

Macron seems to believe that he can actually change Trump's mind on world matters, such as climate change, or the Iran nuclear deal.

And while Trudeau is careful about criticizing any Trump policy that doesn't directly affect Canada, Macron is willing to drive closer to the edge. He believes he can criticize Trumpism the movement, while still staying sweet with the Trump the man.

Macron's speech to the joint session of Congress "was a blatant, frontal attack on Trumpism," says Shribman. "He mixed it with very shrewd references to the Revolution, to the help that France provided to the American Revolution from 1776 on … It was a combination of defiance and embrace."

"It's inconceivable that Justin Trudeau would give a talk like that. It's not part of his character, make-up, inclination, or part of his portfolio. It's a trick that's not part of his game."

Shribman said that is partly because Macron and Trump have something in common that differentiates them from Trudeau, the son of a famous politician who heads an establishment party returning to power.

"Macron emerged in France as, in his way, as much of a disrupter as Trump," says Shribman. "And Trudeau isn't a disrupter. He's part of the restoration in some ways. I think that's the difference."