NOW THAT Donald J. Trump is headed for the Oval Office, a question that attracted much fevered speculation during the campaign deserves more sober consideration: how to handle nuclear deterrence and the valuable alliances that are supported by the U.S. nuclear arsenal. Mr. Trump offered, and then tempered, reckless ideas during his campaign.

Following the election, he has seemed to step away from one of his most disruptive ideas. During the campaign, he suggested the United States might be “better off” if Japan and South Korea went their own way rather than remain under the protective nuclear umbrella of the United States, and called for removing U.S. troops from the region if both nations did not pay more. This might provoke both Japan and South Korea to build their own nuclear weapons, opening a new front of proliferation concerns on top of the threat of North Korea’s expanding nuclear and missile program. But on Thursday, Mr. Trump spoke to South Korean President Park Geun-hye and, according to her office, reaffirmed his intention “100 percent” to uphold the alliance and strengthen it.

Mr. Trump has also raised alarms about his commitment to NATO, and a similarly quick and firm reassurance would be salutary. Mr. Trump’s campaign rhetoric was insular and isolationist, but once in office, he will discover that he needs more than just personal dealmaking skills. Deterrence remains a backbone of American power and influence. There is no sense in sowing doubt among U.S. allies at a time when Mr. Trump confronts very real and sticky problems. How to derail North Korea’s accelerating quest is one of them. It needs a fresh strategy after neglect by President Obama, and it demands more than Mr. Trump’s flip suggestions that he would have China “make that problem disappear,” or that he could solve it by just meeting North Korean leader Kim Jong Un.

Mr. Trump also promised in the campaign to tear up the Iran nuclear accord, but again, there are restraining factors. European partners in the negotiation are not going to return to punishing sanctions on Iran while Mr. Trump pursues a new deal.

At home, Mr. Trump inherits an expensive modernization of the U.S. nuclear arsenal. He seems unlikely to change course, although budget pressures will force hard decisions on some delivery systems.

Russia is the biggest question mark when it comes to Mr. Trump and nuclear weapons. While he and President Vladimir Putin have been exchanging good-natured compliments, it is not clear where that leaves the recent tension over arms control, including U.S. claims of Russian violations of the Intermediate-Range Nuclear Forces treaty or Moscow’s complaints about U.S. ballistic missile defenses. After his contradictory campaign statements about nuclear weapons, Mr. Trump might be wise to follow his own first instinct with South Korea, that is: Preserve what works. Surely, there are going to be enough other disruptive crises to come without creating new ones.