Editor's note: Ofer Zalzberg is a Jerusalem-based senior analyst for Middle East and North Africa at the International Crisis Group. The views expressed are solely those of the writer.

By Ofer Zalzberg, Special to CNN

Newly elected Egyptian President Mohamed Morsy’s call to “update” the Israel-Egypt peace agreement has stirred apprehension in Jerusalem. True, Morsy and other Brotherhood leaders have declared repeatedly that they will respect past agreements and that their focus is the treaty’s military annex. It’s also true that this position was embraced by nearly all other presidential candidates; with the Israeli-Palestinian conflict such a visceral issue, the treaty isn’t likely to disappear from public debate. But long standing Israeli fears about the Brotherhood and its fraternal relationship with Hamas have provoked skepticism among Israelis about Morsy’s intentions in general and altering the annex in particular.

The 1979 treaty imposed limitations on the Egyptian military presence in the Sinai Peninsula in order to restore Egyptian sovereignty without sacrificing Israel’s strategic depth. Today, Cairo argues that formula has turned what was intended to be a buffer zone into a region of lawless mayhem; only the permanent stationing of additional Egyptian military forces, Egypt claims to Israeli interlocutors, will reverse the trend.

Jerusalem rejects this logic: it points to the several times it has endorsed temporary exceptions to the restrictions, and reminds Cairo that it’s free to deploy as many police in the area as it wants. The reigning assumption in Jerusalem is that Egyptian demands to update the annex are motivated by something quite different: the desire to reestablish its national honor by restoring its freedom of action on its own soil. But Jerusalem is highly resistant to relinquishing strategic depth and so waits for Egypt to address the emerging security vacuum in Sinai – certainly a concern for Cairo as well – without changing the treaty or its annex.

There are two chief outcomes to this posturing that could affect not just the military annex, but the future of the treaty as a whole. If the annex isn’t updated, Cairo could drag its feet in cracking down on the chaos, if only because such a move would carry internal costs, draw energy from other burning priorities, and remove the best argument that the government has for altering the formal arrangements. Israel could find itself bordering an anarchic region where Bedouin and others traffic in all kinds of commodities (including armaments and migrants) and militant groups thrive. If cross-border attacks multiply and Jerusalem continues to believe that Egypt is lax, Israel could find itself drawn into a diplomatic and operational morass; among the worst-case scenarios, it could find itself risking a military incursion despite the disastrous implications for Israeli-Egyptian relations.

An alternative would be for Egypt and Israel to negotiate an update of the military annex. Israel surely would object to allowing an unlimited Egyptian military presence in the peninsula, though it possibly could live with more modest modifications such as the permanent stationing of armored personnel carriers, especially if these changes are coupled with enhanced intelligence sharing. Jerusalem worries that the failure of negotiations would jeopardize not only the legitimacy of the annex, but that of the treaty itself. It would therefore be very reluctant to enter such negotiations unless success was all but certain – perhaps secretly agreed in advance.

There’s more to this second scenario than meets the eye. It carries risks, but potentially could yield a significant return both for Israel and the cause of peace. For Jerusalem, the key feature of the deal would be that an increase in Egypt's military presence in the Sinai – with the attendant restoration of national honor – would come only as a result of Morsy’s and the Egyptian parliament’s endorsement of the amended annex and, by extension, of the peace agreement itself. By gaining such assent – particularly should it come with the blessing of the Brotherhood's Supreme Guide – the status of the peace treaty would be enhanced not only among Egyptian officials, but also among public opinion – precisely at a time when it is growing increasingly relevant. Such a step eventually could serve as a precedent, with knock-on effects for Hamas’s opposition to non-Muslim sovereignty on Waqf land.

The choice that confronts Israel today is retaining the hard power of strategic depth and an effectively demilitarized Sinai versus pursuing the subtler gain of the Brotherhood’s political representatives endorsing the acceptability of a peace agreement with Israel. This would entail no small adjustment for the group and require a break with its past positions. But given Egypt’s huge socioeconomic problems, Egypt’s new president will be under pressure to deliver a success, and a foreign policy victory could prove enticing.

The rising Islamist influence in the Arab world by and large has led Israel to pursue a wait-and-see strategy, but the Brotherhood’s newfound prominence has also generated opportunities that Jerusalem should not ignore.