There are reports that Iraqi forces have retaken much of Tikrit, Saddam Hussein’s hometown, from the Islamic State of Iraq and Syria. Pictures of jubilant Iraqi soldiers are appearing on the Internet. It remains to be seen whether these celebrations are premature or not; certainly Iraqi forces have a history of claiming victories over ISIS that soon unravel.

But even if this “victory” stands up, our jubilation should be tightly controlled. Yes, it’s a good thing if ISIS is suffering defeats, but who’s winning? It’s not the United States and it’s not  the lawful Iraqi state led by Prime Minister Haidar al-Abadi. The real victor here, if there is a victory, is Iran. Most of the fighters who are taking Tikrit are Iranian-backed Shiite militiamen, not soldiers of Iraq. The real leader of this operation is not any general appointed by Prime Minister Abadi but rather Qassem Suleimani, head of the Iranian Quds Force, who has been a high-profile presence on the front lines.

And this is not an isolated occurrence. With Iran and its proxies taking the lead in fighting ISIS, there is a real danger that U.S. support for the anti-ISIS drive will wind up delivering Iraq into the hands of Iran. This is, of course, the danger that many opponents of the Iraq War warned about, but it was a danger kept in check as long as there was a substantial U.S. troop presence in Iraq. The U.S. departure at the end of 2011, however, opened the floodgates for Iranian influence.

By focusing U.S. efforts solely on rolling back ISIS, President Obama is providing another opportunity for Iran to expand its influence. This is a very bad development for two reasons: First, the obvious reason–Iran believes that the U.S. is the Great Satan and it is the No. 1 state sponsor of terrorism, with a track record going back to 1979 of mounting terrorist attacks on American targets. So its success in expanding its influence into countries such as Iraq, Syria, Lebanon, and Yemen is a defeat for the U.S.

Second, Iran is anathema to the region’s Sunnis. The more successful that Iran appears to be, the more that Sunnis will flock for protection to ISIS, the Al-Nusra Front, al-Qaeda in the Arabian Peninsula, and other Sunnis terrorist groups.

The U.S. desperately needs a plan not to just to roll back ISIS influence but also to roll back Iranian influence. The kind of plan implemented in 2007-2008 by Gen. David Petraues in Iraq, when U.S. forces targeted Iranian operatives for exposure and arrest. There is, alas, no sign of such a plan today–if anything, the U.S. seems to be tacitly conceding Iran the right to a dominant role in Iraq, Syria, etc., as part of a broader rapprochement that, Obama hopes, will include a nuclear deal.

This is a monstrous mistake. A victory over the terrorists of ISIS in Iraq, even if it is forthcoming, will be hollow indeed if it becomes a victory for the terrorists of Iran.