A "two-state solution" to the decades-old conflict between Israelis and Palestinians is the declared goal of their leaders and many international diplomats and politicians.
It is the snappy shorthand for a final settlement that would see the creation of an independent state of Palestine on pre-1967 ceasefire lines in the West Bank, Gaza Strip and East Jerusalem living peacefully alongside Israel.
The United Nations, the Arab League, the European Union, Russia and the United States routinely restate their commitment to the concept, and US President Barack Obama is sure to do so once again as he visits Jerusalem and Ramallah this week.
But many experts, as well as ordinary Israelis and Palestinians, now believe the two-state option should be abandoned or at least reconsidered.
Twenty years after the breakthrough Oslo Accords there is no sign of a final agreement.
Meanwhile, the construction of Israel's barrier in and around the West Bank and the expansion of settlements on occupied land make a Palestinian state less possible.
On Israel's left and far right in particular, as well as among Palestinian activists, there is renewed talk of a one-state solution.
The Palestinian Islamist movement, Hamas has never officially dropped its claim to a single state in all of historic Palestine.
Some hawkish Israelis, meanwhile, also discuss another alternative: a "three-state solution".
'No longer viable'
Under heavy US pressure, Israel's Prime Minister Benjamin Netanyahu made a speech in 2009, in which he first committed to a "demilitarised Palestinian state".
A year later, peace talks between Israel and the Palestinians were revived but then quickly derailed with the end of a partial freeze on Jewish settlement building.
In recent months, Mr Netanyahu's government has announced plans to construct thousands of new settler homes, including in the sensitive "E1" area that would separate East Jerusalem from the West Bank.
If these go ahead, even the UN has said they would represent "an almost fatal blow" to the chance of a two-state solution.
The noted British-Israeli historian, Avi Shlaim has memorably remarked that Mr Netanyahu "is like a man who, while negotiating the division of a pizza, continues to eat it".
"I've always been a supporter of the two-state solution, but we've reached a point where it is no longer a viable solution," he says. "Now I'm a supporter of a one-state solution, not as my first choice, but as a default solution in the light of Israeli actions."
In recent years, more Israeli leftists and Palestinian thinkers have made the ideological case for a single bi-national state giving equal citizenship and rights to all residents of Israel and the Palestinian territories.
Even some on Israel's right - like the former Knesset Speaker Reuven Rivlin, who is a member of Mr Netanyahu's Likud party - say they would prefer this to a division of the land.
A series of books, articles and conferences have discussed various alternatives - from a power-sharing model similar to that seen in Northern Ireland, or a Bosnia-Hercegovina-type federation where Jews and Palestinians would enjoy a high degree of autonomy.
Last year, the former Palestinian Authority Prime Minister Ahmed Qurei, an architect of the Oslo Accords, said Palestinians needed to start their own debate.
"It could be that despite all the negative aspects and all the differences, we should not rule out the one-state solution as an option," he wrote in the newspaper, al-Quds al-Arabi.
"It should be discussed in an internal dialogue and put to the Palestinian people in a referendum, before it is laid on the negotiating table as an option and thrown in Israel's face like a hot coal because it caused the two-state solution to fail."
'One Strong Israel'
Aware that a one-state solution would undermine the Jewish identity of Israel, frustrated Palestinian officials increasingly warn that they may abandon their quest for statehood and push for that instead.
President Mahmoud Abbas has said there is a danger of "an apartheid-style state" being created.
The argument goes that Muslim and Christian Palestinians - with their growing populations - would quickly outnumber Jewish Israelis. If it acted to raise the status of Jews, Israel would be undermined as a democracy and could end up with an apartheid system. Some claim this exists already.
Several right-wing groups in Israel believe new ways must be found to strengthen a single state of Israel. The "Yes to a Strong Israel" campaign backed by settler groups has a growing presence online and in social media.
"I'm 10 minutes down the road from Jerusalem," says Rut Lieberman from Gush Etzion in the occupied West Bank. "For people who want a two-state solution - cutting up Israel more - this would become Palestine. I'm not sure that works."
"I just drove past a contiguous Jewish population of tens of thousands of people. The two-state solution is a dead end. We have to get it off the table."
Among Israel's 500,000 settlers there is wide support for a plan by the Habayit Hayehudi (Jewish Home) party, which joined the new Israeli government sworn in on Monday.
It proposes annexing the 61% of the West Bank known as "Area C", where Israel already has full military control. Settlers would stay, about 50,000 Palestinians living there would get Israeli citizenship, and the remaining 2.6 million Palestinian residents of the West Bank would be left under autonomous local government.
Last November's conflict in the Gaza Strip brought another idea back into circulation - that of a separation of the Palestinian territories, or the "three-state solution".
Some Israeli analysts suggested that with Hamas governing Gaza - the coastal territory should be stabilised and treated as a state separate from the West Bank, where the Palestinian Authority controls Palestinian areas.
A former Israeli national security adviser, retired Maj-Gen Giora Eiland, has proposed that in order to achieve this Israel should change its long-time policy and talk directly to Hamas.
Others say that Egypt - whose president is a member of the Muslim Brotherhood, which has ideological links to Hamas - should open its border crossings with Gaza and take responsibility for it.
Egypt and Jordan controlled Gaza and the West Bank respectively from 1948 until 1967, when Israel captured them during the Six Day War.
Some right-wing Israelis also posit that for historic reasons, Jordan is Palestine and should provide a home for the Palestinian people. They foresee only three states remaining - Israel, Jordan and Egypt - which have already signed peace treaties.
Such a neat formulation overlooks the fact that Cairo, Amman and the Palestinians themselves would never agree to it.
"Palestinians will never melt into another entity or identity," says Mahdi Abdul Hadi of the Palestinian Academic Society for the Study of International Affairs.
"Especially after all these years of occupation and struggle and sacrifice, Palestine cannot be moved and placed in someone else's lap."
Much to the annoyance of Israel and the US, Palestinians were granted the status of a non-member observer state at the UN General Assembly in November.
This has earned them the right to use the designation "State of Palestine" on UN documents and possibly to challenge Israel's occupation of Palestinian land before international courts.
However, in real terms a sovereign Palestinian state remains as elusive as ever.
An opinion poll carried out last November suggested that the number of Palestinians supporting a two-state solution remained steady at 51%. But support for a bi-national solution had risen to 27%, up five percentage points from the previous year.
There are serious doubts - on both sides - about whether President Obama can achieve anything and whether he can be trusted.
An Israel Democracy Institute poll this month found that 62% of the Jewish public believed he lacked the ability to bring a real breakthrough in relations with the Palestinians.
As Mr Obama will no doubt find, Israeli and Palestinian leaders are divided among themselves about how to proceed and ongoing political turmoil in the region confuses the situation further.
At the same the conflict continues to fester and cannot be ignored.