As the U.S. begins to reimpose tough sanctions on Iran, defenders of the 2015 nuclear deal are peddling myths. They say Russia, China and India will evade sanctions. They claim oil prices will skyrocket. And they predict Europe will establish a “sanctions free” payment channel to Iran. None of these warnings should slow President Trump’s campaign to impose maximum pressure on the Islamic Republic.

Since the U.S. withdrew from the Joint Comprehensive Plan of Action in May, major companies like Siemens, Total and Maersk have...