(RNS) Pope Francis is being hailed around the world — and criticized by some in the U.S. — for his pivotal role in brokering the historic breakthrough in relations between Washington and Havana, a role attributed to his background as the first Latin American pope and to the special position he occupies.

“Pope Francis did what popes are supposed to do: Build bridges and promote peace,” Miami Archbishop Thomas Wenski said after the announcement Wednesday (Dec. 17) about the U.S.-Cuba rapprochement.

Yet, as with most surprises, there are other, often less obvious factors that help explain how this happened. Here are three:

1. You’ve got to be in it to win it

The Vatican’s push to normalize relations between Havana and Washington isn’t some policy Francis suddenly invented; for decades popes in Rome and bishops on both sides of the Florida Straits have been urging the U.S. to take this step, and Cuba to change its repressive ways.

But since he was elected in March 2013, Francis has persistently moved to return the Vatican to the global stage to a degree not seen since the 1980s, when St. John Paul II’s shuttle pilgrimages between East and West helped end the Cold War.

Francis has, for example, hosted Israeli and Palestinian leaders at the Vatican, held public vigils for peace in Syria and called for action to resolve conflicts in South Sudan, the Central African Republic and Ukraine.

He also put the Vatican diplomatic machinery to work; he began pressing the U.S. and Cuba to make peace months after he was elected and never let up.

“Francis is not resigned to a passive vision of world affairs,” said Marco Impagliazzo, president of the Rome-based Community of Sant’Egidio, a Catholic organization active in conflict resolution and peace brokering. “We must prepare for a new age of political audacity for the Holy See.”

2. Diplomacy is the gospel

When Pope Benedict succeeded John Paul in 2005, he brought with him the team he’d had with him during his years as the Vatican’s top doctrinal overseer, namely Cardinal Tarcisio Bertone, who he named secretary of state — though Bertone said he hoped to be a secretary “of Church.”

“Less diplomacy and more Gospel,” is how veteran Vatican-watcher Sandro Magister summed up Benedict’s foreign policy.

That didn’t work out so well, either for the gospel — Bertone presided over a series of scandals and crises that seriously undermined the Vatican’s reputation — or for church diplomacy.

Francis has taken a much different tack, bringing back experienced church diplomats and putting them in senior positions. Chief among them is Cardinal Pietro Parolin, a former Vatican ambassador to Venezuela who is now Francis’ secretary of state, and Archbishop Giovanni Becciu, whom Francis appointed as the Vatican equivalent of foreign minister.

Becciu was most recently the Vatican’s representative in Havana; he and Parolin took a close and active interest in advancing the U.S.-Cuba talks.

The work of diplomats “is a job of taking small steps, doing small things but whose aim always is to build peace, to bring the hearts of people closer together and sow brotherhood between peoples,” Francis said Thursday in brief remarks to new ambassadors to the Vatican.

“Yours is a noble, very noble work,” he said.

3. The U.S. political — and religious — landscape has shifted

Engaging Cuba is not the third rail of American politics that it once was: Demographic shifts among Latinos, even in the once firmly anti-Castro community of Cuban emigres, have altered the domestic political realities in Florida and nationally.

Also, Francis is not fighting the last war — the one between the White House and the U.S. Conference of Catholic Bishops, whose relations went south over issues such as gay rights and the contraception mandate. The pontiff has from the beginning been interested in engaging the Obama administration, and the rest of the world, and many of his priorities — on economic justice and international relations — line up with the president’s.

That shift in Rome may also bring the USCCB along, at least to some degree. The bishops not only welcomed this latest move on Cuba, but last month they also praised Obama’s recent executive actions on immigration. In fact, the USCCB’s president, Louisville Archbishop Joseph Kurtz, was at the White House on Tuesday, the eve of the Cuba breakthrough, for his first meeting with Obama and Vice President Joe Biden.

That’s the sort of constructive interaction that has been missing in the relationship, and if it continues it can serve both parties: The face of the Catholic Church is increasingly Latino, and so is the Democratic base.

To be sure, if there is no emerging grand alliance like the one that was said (and perhaps overstated) to have bound John Paul and Ronald Reagan in their efforts against Moscow, there are shared interests and visions that can produce concrete results.

“I want to thank His Holiness Pope Francis, whose moral example shows us the importance of pursuing the world as it should be, rather than simply settling for the world as it is,” Obama said in his remarks on Wednesday.

At the same time, Francis’ effort has discomfited the bishops’ longtime allies in the Republican Party.

Case in point: Sen. Marco Rubio, whose parents are from Cuba, and former Gov. Jeb Bush are both from Florida, both Catholics and both considered GOP presidential contenders. Both blasted Obama’s deal.

That’s a problem. “When Republicans are attacking Obama on Cuba,” tweeted Political Wire publisher Taegan Goddard, “they’re also attacking Pope Francis.”

And Francis is a lot more popular than any U.S. politician.

Three other questions remain:

What’s next for Francis? In many respects, the Cuba deal was the low-hanging fruit of diplomatic breakthroughs, given Francis’ Latin American background and the other political dynamics involved. As John Paul said of the Soviet communism he helped doom: “The tree was already rotten. I just gave it a good shake.” Most conflicts today, by contrast, are bloodier and nastier, more tribal than ideological, and more intractable.

Will Francis visit Cuba next year? That’s the question many are asking. He has said he expects to visit three Latin American countries in 2015 — and he will visit the U.S. in September. This month Francis also pushed U.S. Secretary of State John Kerry to close the Guantanamo detention center on the U.S. base in Cuba. Achieving that goal would give the pope an added incentive to visit the island nation on his way to or from Rome.

Will he get a Nobel Peace Prize? Not likely. Mother Teresa got one in 1979 and the Dalai Lama in 1989, but no pope has ever received the award. And if John Paul didn’t get it for helping bring down the Berlin Wall, it’s hard to see Francis getting one for thawing the Washington-Havana Cold War.