For the first time in a generation, there is widespread anxiety about the possibility of nuclear war, stimulated by the extreme tensions between North Korea and the United States. Secretary of State Rex Tillerson has advised Americans that they can sleep safely at night, a reassurance that most people probably wish they did not need to hear.

Mr. Tillerson offered his soothing counsel to deflate media hype about recent threats and counterthreats exchanged between Pyongyang and Washington. His words also reflect profound unease about the temperament and judgment of the two leaders who could trigger inadvertent war: President Trump and Kim Jong-un.

Mr. Trump and Mr. Kim appear to believe that bombast serves their domestic needs. Both seem to think that they can dominate and intimidate through the direst of threats. However, words can easily have consequences that neither leader seems to grasp.

Should we be living in a world where two leaders can stumble into a nuclear holocaust? North Korea’s accelerated pursuit of nuclear weapons clearly requires a much-enhanced containment and deterrence policy by the United States and its allies to prevent Mr. Kim from undertaking ever-riskier options. But what can be done to constrain the actions of an American president whose stability is now openly questioned, even by the Republican chairman of the Senate Foreign Relations Committee, Bob Corker of Tennessee?