But a nuclear deal is not going to prevent conflict either. The presidency of the so-called pragmatic mullah Ali Akbar Hashemi Rafsanjani from 1989 to 1997 was an aggressive period of Iranian terrorism. If President Rouhani, Mr. Rafsanjani’s former right-hand man, can pull off a nuclear agreement, we are likely to see a variation of the 1990s Iranian aggression.

Such aggression has already begun. Revolutionary Guards are fighting in Syria and Iraq, and Iranian aid flows to the Shiite Houthis in Yemen. Wherever the Islamic Republic’s influence grows among Arab Shiites, Sunni-Shiite conflict grows worse. With greater internecine Muslim hostility, the clerical regime inevitably intensifies its anti-American propaganda and actions in an effort to compete with radical Sunnis and their competing claims to lead an anti-Western Muslim world.

Iranian adventurism, especially if it includes anti-American terrorism, will eventually provoke a more muscular U.S. response. The odds of Tehran respecting any nuclear deal while it pushes to increase its regional influence—unchecked by Washington—aren’t good.