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In his , US President Barack Obama offered an invitation to the world’s most closed countries. “We will extend a hand,” he said, “if you are willing to unclench your fist.” This statement encapsulated the foreign policy of “engagement” that he endorsed during his first term – an approach that, despite some shortcomings, has a lot of merit.

Obama rejected his predecessor George W. Bush’s policy of isolating “rogue states,” recognizing that America’s only hope for influencing isolated countries’ behavior was to engage directly with them in a bilateral context. And, as a bilateral strategy, engagement has proved to be astonishingly successful, having led to historic openings, first to Myanmar and now to Cuba, while driving progress toward an enduring .

From the beginning, however, the Obama administration has made clear that engagement is not an end in itself, but a means to various goals, both bilateral and regional.

In Myanmar, the bilateral goal was to nudge the government toward greater openness and democracy – something that has unquestionably happened. The pro-democracy leader and Nobel laureate Aung San Suu Kyi was released from house arrest; her party won seats in parliament; and millions of Burmese are now studying their country’s constitution and have petitioned for amendments.

To be sure, much remains to be done. The journalist Myanmar as a “halfway house between military and civilian rule,” observing that the country’s generals have been promising to complete the transition to democracy for several years now, yet remain unwilling to allow Suu Kyi to run for President.

But this should not obscure the progress that has been made; compared to 2009, when Obama took office, Myanmar and its politics are unrecognizable. While Obama would likely acknowledge that US policy did not bring about these changes (which resulted from an internal process of recalculation by the president, General Thein Sein), the US was responsive and flexible enough to encourage them.

On the regional front, Obama hoped that an opening with Myanmar would ensure that the country did not become wholly dependent on China, while enabling the US to deepen its relationship with the Association of Southeast Asian Nations. The resumption of diplomatic relations with Myanmar was a critical feature of the Obama administration’s .

As for Cuba, Obama’s primary goal seems to be to bolster respect for ordinary Cubans’ human rights, not to bring about regime change. While it is too soon to assess the opening’s impact in terms of reducing repression, the opportunity it presents for Cubans to engage with Americans – first family to family, then business to business – is significant.

In regional terms, Obama’s restoration of relations with Cuba merits a place in the history books alongside Richard Nixon and Henry Kissinger’s opening to China. As grandiose as that claim may seem, the fact is that crossing the straits to Cuba signals a new, more open, and far more productive approach to relations with all of Latin America.

Over the last decade, US leaders’ efforts to establish productive frameworks for multilateral cooperation with Latin America – including attempts to and build up new forums like the – have run aground on their continued isolation of Cuba. Indeed, the 2012 Summit of the Americas in Cartagena became an exercise in America-bashing, with countries threatening to boycott the 2015 summit if Cuba was not invited.

Fortunately, the US stepped up to the challenge, and, with Cuba at the table, the summit was held . As a result, the Summit of the Americas and other regional organizations are better positioned to address regional crises, like the coming meltdown in Venezuela, and opportunities, such as the establishment of a hemispheric energy, trade, and law-enforcement infrastructure.

A nuclear deal with Iran would have similarly important implications in the Middle East and Southwest Asia – a prospect that largely explains fervent opposition to negotiations by Israel and Saudi Arabia. While the deal will stand or fall on the extent to which it pulls Iran back from the nuclear brink, it can also open the door to further bilateral negotiations on matters of common interest, from ending the war in Syria to cracking down on drug-running in Afghanistan. Already, Obama’s policy of engagement has led to the most bilateral interaction since the Iranian revolution and hostage crisis in 1979.

Whatever America’s Republican Party tries to claim during the 2016 presidential election campaign, Obama’s policy of engagement has worked, enabling the US to shape events in even the most closed countries. So why do pundits continue to debate America’s supposedly declining global influence? (Just last week, the topic made the front page of the New York Times, in that quoted a former treasury official as saying, “We’re withdrawing from the central place we held on the international stage.”)

One answer is that domestic political dysfunction has severely handicapped the president in international negotiations. For example, the US Congress has blocked changes to countries’ quota allocations at the International Monetary Fund. And a group of 47 Republican senators wrote announcing that the next Congress may not honor whatever nuclear deal they reach with Obama.

Another source of doubt about America’s enduring influence lies in the fact that multilateral engagement is still needed, and this is always more difficult than bilateral engagement. Indeed, multilateral leadership requires not only clearer and bolder rules, but also a demonstrated willingness to bear the costs of those rules, whether by creating safe zones to uphold the or taking concrete steps to reduce – and eventually eliminate – .

Bilateral engagement will prove to be one of Obama’s most important foreign-policy legacies. But ensuring that the US can continue to lead in the twenty-first century will require a different kind of engagement. That will be a critical task for America’s next president.

This article first appeared in .