The old: Olmert took over after Sharon suffered a massive stroke in 2006
Israeli prime ministers tend to have a pretty short shelf life, but the issues they grapple with seem immutable.
Only Ariel Sharon has won successive elections in the modern era, albeit at the head of two different parties; fate has decreed that no-one else would last even four years as PM since the early 1990s .
Ehud Olmert succumbed after less than three, brought down by a mix of corruption allegations and his poor war leadership.
But while the Olmert years may have seen a new low in the public perception in Israel of its political leaders, since the 2006 Lebanon war his stewardship of foreign policy tells another story.
Just maybe, some people thought, Mr Olmert would enable Israel to settle accounts with its foes and head towards a more secure future.
The outgoing PM still intends to do a deal with Palestinian leader Mahmoud Abbas, a man he is said to have developed a warm personal relationship with, before he steps down in two months.
But the challenges seem as daunting as ever, and it will be all the more difficult in a expected period of political turmoil with no obvious successor and ambitious contenders vying for power.
Peace hopes have been raised through an assortment of negotiations, initiatives, prisoner swaps and ceasefires.
Calm reigns on the northern front with Lebanon and even the situation in Gaza and southern Israel has quietened.
Israelis view the Golan, seized in 1967, as an integral part of their country
Perhaps the most significant initiative has been the indirect talks with Syria over the fate of the Golan Heights.
Secretive, Turkish-mediated contacts were always likely to be part of a long process that could easily fall prey to ructions in Israeli politics.
Indeed the president of Syria - a country with considerably longer-lasting leaders - said Damascus would wait for a new US administration before engaging in direct talks.
The big question is whether Israel can face giving up the Golan, valued as a strategic asset (and cherished as a fantastic leisure amenity by Israelis) since its forces captured the territory in the 1967 war.
Damascus too must ponder Israeli demands it breaks ties with Israel's main foes, Palestinian and Lebanese militant groups like Hamas and Hezbollah, and Iran.
Contenders and conundrums
There is no way of knowing if Damascus is serious about realigning itself - rewards could be great, but so could possible repercussions.
For Israel, the Kadima party frontrunner to replace Mr Olmert, Foreign Minister Tzipi Livni, is most likely to keep the talks with Syria running.
The new: Mofaz and Livni are front-runners to replace the PM
By contrast her closest rival, hawkish transport minister and former army chief Shaul Mofaz, is not known as a land-for-peace advocate, so the momentum may be lost.
The same goes for Likud leader Binyamin Netanyahu, the right-wing former PM who is a contender again if fresh elections are called.
Analysis of their positions on Syria - Livni/continuity, Mofaz and Netanyahu/a tougher stance - can be translated to the Palestinian file.
But with the Palestinians it is much less clear how problems can be solved, over Jerusalem, Jewish settlements, the borders of a Palestinian state.
Add to that Hamas control of Gaza, Palestinian refugees and Israel's "demographic time-bomb" - the eventuality that Jews will become a minority within the Jewish state - and, frankly, the mind boggles.
Finally there is Iran, feared to be developing a nuclear weapons capability - something Israel is already thought to possess - and frequently uttering blistering denunciations and threats against Israel.
Mr Mofaz is the one to watch, having promised in June that "if Iran continues its nuclear weapons programme, we will attack it".
However, any Israeli leader's position may be bound by events to the West rather than to the East.
Washington also installs a new leader in the next six months, and the outcome of US elections, as much as anything that happens in Israel, could have great bearing on its policy toward Iran and all the other big issues.