The Houthis, Shiite Muslim rebels who announced that they were taking control of Yemen’s government last week, don’t seem much like natural allies of the United States.

One of their favorite slogans is “Death to America, death to Israel, damn the Jews.” U.S. officials say they’ve received money, weapons and training from Iran. An Iranian official boasted recently that thanks to the Houthis, Yemen’s capital is now “in the hands of Iran,” along with those of Iraq, Syria and Lebanon.

And yet, last week, Obama administration officials were scrambling to contact Houthi leaders and assure them that the United States doesn’t consider them an enemy. “We’re talking with everybody,” an official told me – “everybody who will talk with us.” The Houthis’ top leaders haven’t been willing to meet so far, but the Americans are working on it.

Why so much eagerness for a working relationship with a group that wants less U.S. influence in its homeland, not more? Because the Houthis and their allies are now in charge in Yemen, one of the main battlegrounds in the long U.S. war against al-Qaida. And the Houthis hate al-Qaida.

U.S. officials consider the al-Qaida branch in Yemen a bigger threat than any other terrorist group because of its penchant for long-distance attacks against Americans. Al-Qaida in the Arabian Peninsula, as the group is known, has made several attempts to explode bombs on U.S. airliners, although none has succeeded.

The Houthis are Shiite Muslims and al-Qaida is rigorously Sunni, but the antipathy isn’t mainly sectarian; it’s an old-fashioned struggle over territory and power. The Houthis have ruled most of northwestern Yemen for centuries, and they’ve been alarmed by al-Qaida’s incursions to their south. The two factions have already fought battles on the ground. One of the Houthis’ complaints against the Yemeni government they just overthrew was that it wasn’t putting enough force into the battle against al-Qaida. Last week, al-Qaida issued a statement accusing the Houthis – a little prematurely, perhaps – of being “faithful partners of the United States.”

In other words, for the U.S., the enemy of my enemy is my friend. But what about the Houthis’ Iran problem? Should we be worried that the enemy of our enemy al-Qaida is also friends with our other enemies – adversaries, anyway – in Tehran?

“Iran is on the march,” Sen. John S. McCain, R-Ariz., warned last week. “In Yemen, it’s not AQAP that’s taken over the government, it’s the Houthis.” McCain said the solution was “more boots on the ground” – not a U.S. invasion force, but special operations forces.

Obama administration officials insist that those fears are overblown. The Houthis “get support from Iran, but they’re not controlled by Iran,” one official told me last week.

Houthi leaders dissolved Yemen’s parliament Friday after weeks of political negotiations deadlocked. Now they are trying to form a new transitional government, and they say it will include representatives of most of the country’s factions. (Only about a third of Yemen’s 25 million people are Houthis; a Houthi-only government would win little support in the Sunni south.)

The central question for U.S. officials is whether that next government can be persuaded to join in counterterrorism against al-Qaida at all – let alone as enthusiastically as the last government.

That was tested over the last two weeks as the United States resumed drone strikes in Yemen after a pause of several months amid the political chaos in Sana.

U.S. officials said they were pleased to find that there was no discernible reaction. But that acquiescence seems unlikely to last. Houthi leaders have long denounced U.S. drone strikes as an invasion of Yemen’s sovereignty; they say they can handle al-Qaida themselves.

And American experts on Yemen say the drone strikes are widely unpopular. “It really has fueled tremendous resentment,” said Stacey Philbrick Yadav, a professor at Hobart and William Smith Colleges who has lived in Yemen. “I have never met a (Yemeni) defender of the strategy. It’s not criticism; it’s more like repulsion.”

Indeed, the drone strikes may have been a factor in the fall of Yemeni President Abdu Rabu Mansour Hadi, who pleased U.S. officials with his open endorsements of cooperation with the United States but proved incapable of retaining support among his own country’s political factions.

In President Barack Obama’s view, there’s no alternative to trying to keep the partnership alive. But as U.S. diplomats wait hopefully for their appointments with Yemen’s new Houthi power-brokers, they may want to remind themselves of some old lessons about power politics in the Middle East:

Be careful before you claim any model as a success (as Obama said of Yemen only last fall) – you may live to rue those words.

When a shaky government declares itself your ally, as Hadi did, that doesn’t mean it has acquired extra wisdom. And the enemy of your enemy may be your friend today, but that doesn’t make him your friend forever.