Israel and Saudi Arabia have an odd relationship, and people are talking about it going into even weirder places—like a strategic alliance.

On the surface, Israel and Saudi Arabia have obvious overlapping areas of interest. Specifically, they have common enemies: fundamentalist Shi’ism in the form of Iran and Hizbullah, and al Qaeda. They also share a desire for stable regional governments and are not motivated by the pursuit of liberal values in their foreign policies. Lastly, they are both worried about the direction of American security policy in their region—both because of the present security crises facing these countries and because they fear the U.S. is withdrawing from its overall commitment to the region.

With these common sources of anxiety, commentators have speculated about an alliance between the Jewish State and the custodians of the holy cities of Islam. Iranian TV has even excitedly promoted this possibility in an effort to discredit the Saudis.

The reality is that the space for further Saudi–Israeli cooperation is limited. Even setting aside the Palestinian issue, differences in priority, capability, and method in pursuing their interests are obstacles to better relations.

Take Syria. The Assad regime is seen by both countries as an extension of Iranian influence, and its potential overthrow as a great setback for Iran and Hizbullah—but the worst-case scenario in Syria is different for each country. The last thing the Saudis want is continued Assad/Alawi rule. But Israel is even more fearful of a total power vacuum that allows (and encourages) Salafi jihadis to attempt terrorist attacks on Israeli territory. Armament of the rebel Islamist forces with advanced weapons, as the Saudis are now undertaking, poses a potential future threat to Israel.

The Saudis want the conflict to end as soon as possible. Israel, meanwhile, actually benefits by having Hizbullah drawn into a messy conflict in which the Jewish state plays no part.

To illustrate how simple geography creates differences, look at the Russian initiative to disarm Assad of his chemical weapons. Although the proposal caught Tel Aviv and Riyadh off guard, as did the American embrace of it, the security effects are not the same in each country. Syria and Israel share a land border, and Israeli population centers are within range of Syrian ballistic missiles. Saudi Arabia does not share a border, and its population centers are far from Syrian missile range. The elimination of the chemical stockpile (once complete) will thus be a major security boost for Israel, while Saudi Arabia will see little direct benefit.

Another problem inhibiting a closer alliance is that Israel’s potential contributions to addressing Saudi security concerns are minute. In Saudi eyes, the best thing Israel could do for the Kingdom is resolve the Palestinian issue as soon as possible. But this priority clashes with one of Israel’s central security concerns, which is to minimize the risk of Palestinian political violence. Other Saudi priorities, such as the stability of the Bahraini monarchy, naval freedom in the Persian Gulf, the subservience of domestic Shi’a populations, and related matters, are not topics that Israel can assist the Saudis with.

Likewise, the Saudis could not be a meaningful sponsor of Israeli defense should the U.S. scale back its regional involvements; Israel is in a much stronger position of defense preparedness than Saudi Arabia is. Any other potential favors the Kingdom could do for Prime Minister Netanyahu, such as by softening anti-Israel rhetoric in Middle Eastern political fora, are not options without progress on the Palestinian front.

Whatever behind-the-scenes communications exist between Israel and Saudi Arabia will certainly continue and may intensify as Iranian nuclear diplomacy levels. Still, each country will continue to push its own agenda. For the foreseeable future, any cooperation will be ad hoc and private.