His special envoy makes clear the administration’s priority is depriving the regime of nuclear weapons.

Before President Trump announced in Tuesday’s State of the Union address that he would hold another summit this month with Kim Jong Un, he indulged in a bit of braggadocio: “If I had not been elected president of the United States,” he said, “we would right now, in my opinion, be in a major war with North Korea.”

That may sound strange coming from a president whose engagement with North Korea began with insults and threats, with Messrs. Kim and Trump calling each other “dotard” and “Little Rocket Man.” But Mr. Trump’s alternative history aside, his administration has indeed pursued serious diplomacy with North Korea, taking a novel approach that will shape the bilateral relationship far into the future.

The new tack was made clear in a detailed speech given at Stanford last week by Stephen E. Biegun, the U.S. special envoy to North Korea. Mr. Biegun firmly reiterated the administration’s objective: “the final, fully verified denuclearization of North Korea.” Of course that’s easier stated than accomplished, but the administration has set a standard, and has exposed itself to harsh criticism if it tries to deliver anything less.

This approach compares favorably with the one the Obama administration took toward Iran, never demanding an end to nuclear programs and settling for a deal that came nowhere close. When Mr. Trump ditched the Iran deal before engaging North Korea, he signaled his commitment to stricter terms in his talks with Mr. Kim. Mr. Trump’s critics assume the administration will settle for cosmetic changes rather than denuclearization, but its actions and its unified message lay down a very different marker.

Mr. Biegun’s speech also made clear that, although America’s policy objective in North Korea is large, it is also limited: the elimination of the nuclear threat, not the transformation of North Korea. “It is an understatement to say that our two systems are very different,” Mr. Biegun said. “We have dramatically different views on individual rights and on human rights.”

The North Korean government is truly monstrous, but the most dangerous problem it poses comes from its nuclear-weapons programs, and U.S. diplomacy must concentrate there. Mr. Kim has it clear that his motive for pursuing nuclear weapons is security, and the Trump administration would bolster his sense of insecurity by pressing for internal transformation. To Mr. Kim, that would sound like a case for regime change.

Mr. Biegun was even more blunt in the question-and-answer period after his speech. “I don’t mince my words when I say that [Mr. Trump] is unconstrained by the assumptions of his predecessors,” he said. “President Trump is ready to end this war. It is over. It is done. We are not going to invade North Korea. We are not seeking to topple the North Korean regime.” Disapproval of North Korea is not a policy, and the expression of disapproval is not diplomacy.

The special envoy also made clear that the diplomacy between the U.S. and North Korea is personal. He described negotiations as “top down”—the product of commitments Messrs. Trump and Kim personally make to each other. Usually political leaders meet only after subordinates have ironed out details.

President Trump’s diplomacy is in some ways more 19th-century than 21st. He has shed President Obama’s view that history has a “right side,” which America’s rivals will eventually seek to join. Mr. Obama’s Iran deal was premised on Tehran’s voluntarily abandoning its radicalism and deciding to join the peaceful, modern world. The Trump administration makes no such assumption about North Korea’s eventual benevolence.

Finally, Mr. Biegun’s speech was refreshingly honest about the possibility that this effort may not succeed. “It is a cliché to say that failure is not an option,” he noted. “I have intentionally not focused on the many ways that this could all fail. As the diplomatic record of the past 25 years shows, they are too numerous to count.”

What happens then? “We need to have contingencies if the diplomatic process fails, which we do,” Mr. Biegun said without elaborating. But in addition to the carrot of “a bright future for the Korean people” in exchange for denuclearization, the U.S. has always has sticks ready as well.