The United States carried out a new military strike against Houthi ballistic missiles in Yemen on Tuesday, the U.S. military said, but the latest salvo against the Iran-backed group left the White House grappling with how to stop a battle-hardened foe from disrupting shipping lanes critical for global trade.

The strikes on Tuesday, the third overall against the group since a U.S.-led air and naval barrage hit dozens of targets last week, destroyed four missiles that the Pentagon’s Central Command said posed an imminent threat to merchant vessels and Navy ships traveling through the Red Sea and nearby waters.

But the pre-emptive American strike also came on the third day in a row the Houthis have defied the Biden administration and its allies by firing missiles at passing ships, damaging a Greek-owned cargo vessel on Tuesday. The Houthis damaged a U.S.-owned commercial ship on Monday after attempting to hit an American warship the day before.

“We’re not looking for a war; we’re not looking to expand this,” John F. Kirby, the National Security Council spokesman, told reporters on Tuesday, adding, “We will continue to defend against them and counter them as appropriate.”

That leaves the administration with difficult choices. President Biden could order another blitz of strikes against Houthi air defenses, weapons depots, and facilities for launching and producing an array of missiles and drone, but analysts say that would risk widening the war even more. Or he could settle for more limited tit-for-tat exchanges, like Tuesday’s strike, but that would not necessarily resolve the threat to commercial ships, analysts say.

Neither approach has fazed the Houthis so far. Vowing solidarity with Palestinians in Gaza, the group’s leaders have said they will continue their attacks in what they say is a protest against Israel’s military campaign in the territory.