The surprising thing about Ehud Olmert's announcement on Wednesday was not his declared intention to resign in September as Prime Minister of Israel after just two years in office; it's that he managed to last this long. Olmert's handling of the botched Lebanon war in the summer of 2006 plunged his approval ratings into the single digits, and he never really recovered the confidence of the Israeli electorate. Still, he hung on, even when he became the target of a criminal investigation into corruption allegations, promising to resign in the event of an indictment. Some will see the fact that he has chosen to do so now, making clear that he will not be a candidate when his Kadima Party holds a primary to choose a new leader in September, as a sign that charges may be in the offing over the case of U.S. businessman Morris Talansky, who has admitted to giving Olmert large undeclared donations.Politically speaking, Olmert may have been a dead man walking for more than a year now, but leaving an enfeebled and unpopular Prime Minister in place may have suited most of his potential successors, each of whom who has used the intervening period to burnish his or her own claims. And despite his dire domestic political prospects, Olmert focused his energies on Israel's relations with its neighborhood. He has called time on his tenure at a moment when he is engaged in talks with Palestinian Authority President Mahmoud Abbas over the terms of a future peace agreement, as well as indirect negotiations with Abbas' rivals in the Hamas movement that controls Gaza and also with Syria. He has also been lobbying international support (particularly the U.S.) for tough action to deter Iran from pursuing nuclear weapons. So how will all these issues, which could have major regional and international consequences, play out without him at Israel's helm?In short, very little is likely to change on any of those fronts. The significance of Olmert's talks with Abbas, at the behest of the Bush Administration, were routinely overstated. The Palestinian leader may not have substantially greater standing among his own people than Olmert does in Israel, yet the talks were confined only to Abbas' Fatah organization — which is not actually at war with Israel — and were expressly designed to avoid Hamas, which remains engaged in confronting Israel. And their purpose was not to arrive at a deal for implementation, but rather to achieve a hypothetical settlement that would be shelved for a better day. Many in the region saw the Olmert-Abbas talks as more reflective of a U.S.-Israeli effort to isolate more militant elements that might be allied with Syria and Iran than of any serious intent to expeditiously resolve the Israeli-Palestinian conflict. The irony, of course, is that those elements the U.S. and Israel had hoped to isolate have done a lot better over the past couple of years than have politicians like Abbas who enjoy U.S. favor.Pragmatic objectives such as halting Palestinian rocket fire out of Gaza and recovering a kidnapped Israeli soldier being held there have prompted the Israelis to abandon their own taboo against dealing with Hamas and negotiate a cease-fire via Egypt. Those pragmatic imperatives will remain even after Olmert has left the scene, as will the ones that prompted Israel to begin negotiating with Syria via Turkey this past spring, in the hope that Damascus can be detached from Iran — something officials close to the Syrian leadership have told TIME will not happen. And the effort to press for action against Iran was never dependent on Olmert's own political standing.Still, Olmert's departure may bring on a new episode of political instability in Israel. His party, Kadima, has little by way of a defining political identity, having been created by a grouping of breakaway pragmatists from the right-wing Likud Party and held together by the forceful personality of Ariel Sharon — who remains in a coma more than two years after suffering a stroke. Olmert's successor as party leader could be the more dovish Foreign Minister Tzipi Livni or the hawkish Transportation Minister and former army chief Shaul Mofaz. Nor is it clear that whoever Kadima chooses will automatically assume the reins of government; the coalition that kept Olmert in power could break apart. Right now many polls show that a new election could just as easily return the even more hawkish Likud leader Benjamin Netanyahu to power. (Both Mofaz and Netanyahu have advocated military action against Iran's nuclear program.) Whatever his personal failings as a leader, Olmert's tenure was a reflection of a long-term stalemate in Israeli politics, in which no party is capable of governing without the support of a phalanx of others who don't share its perspectives and intentions.That post-Sharon political drift, combined with the serial reversals suffered by the Bush Administration across the Middle East — and its lame-duck status as the region waits for a new U.S. President — may at least explain why Israel's political class had been willing to allow Olmert to stumble on for so long. Now, Israel's leaders will be forced to forge a new equilibrium in a more testing time.— With reporting by Aaron J. Klein / Jerusalem