Both men would like to see the back of Hizbollah - Mr Sneh rather more urgently than Mr Al Amin. But here ends this unlikely Israeli-Lebanese accord, for they disagree about how best to achieve it.
'As long as Lebanon is a nest for terrorists we must stay there. It is like spraying the cockroaches in the kitchen, you have to keep doing it,' said Mr Sneh, a Labour MP and an influential member of the Knesset foreign and defence committee.
'As long as the Israelis occupy the land there will be support for the resistance; when Israel goes they will have to go too,' said Mr Al Amin.
Giving their prognosis for a resolution on the Lebanese front, as tension rose once again in the area, neither Mr Sneh, sitting in the cafeteria of the Knesset in Jerusalem, nor Mr Al Amin, in his office in the southern Lebanese town of Tyre, displayed any hope. Hizbollah had just launched new attacks on Israeli and Israeli-backed forces, which occupy a strip of southern Lebanon as a buffer zone against cross-border attacks. As usual, Israel warned of its readiness for massive retaliation.
From the sound both of the shelling and of the rhetoric that always follows like a booming echo, nobody would know that southern Lebanon is currently a subject of the Arab-Israeli peace negotiations.
It is one of the many anomalies of the peace process that southern Lebanon - the most war-like front in the conflict today - is hardly discussed at all. In theory, south Lebanon should be discussed by Israel and Lebanon. But as Lebanon cannot move without the say-so of Syria, in practice it should be discussed directly between Israel and Syria. However, to do so would be to question Lebanese sovereignty. Furthermore, Syria is happy that the issue is kept down the agenda in the peace talks. Syria's prime concern is the return of the Golan Heights.
Israelis have questioned Syria's commitment to peace. For while its diplomats are talking face to face with Israelis in Washington, forces under its protection are killing Israelis in southern Lebanon. Syrians see no inconsistency in this approach. Rather, they consider support for Hizbollah as strengthening their negotiating position with Israel to obtain concessions on the Golan Heights. Syria also keeps 40,000 troops on Lebanese soil.
If serious proposals were to be put forward, the Lebanese-Syrian plan would demand Israeli withdrawal as a prerequisite of any peace. The South Lebanon Army, a Lebanese militia about 3,000-strong, recruited, trained and commanded by Israel to man the front line in the buffer zone, would be amalgamated into the fast-growing Lebanese army. Unifil, the United Nations peace-keepers in the area, would go home.
Moderates such as Mr Al Amin say Israel need have no fears about future security, as the Lebanese army would move south, taking control in the villages of southern Lebanon and disarming Hizbollah, as it has successfully disarmed other Lebanese militias in recent months. 'The only dream of the people is to see the Lebanese army take control,' he says. His claim that the Lebanese army is an increasingly effective force is supported by many experts, including Unifil.
Moderates such as Mr Al Amin argue the Lebanese army would have no problem disarming Hizbollah, who would instantly lose support once their only reason for being in the area - resistance to Israel - had gone. At the same time Syrian forces would also be able to leave Lebanese soil. Palestinian militias would return 'to Tunis or Germany', says Mr Al Amin. And Palestinian refugees in the Lebanese camps would 'go home'.
To the likes of Mr Sneh such a scenario is 'highly theoretical' and, in parts, simply naive. The Israeli general agrees that the Lebanese army is improving and 'is less sectarian'. He also agrees that the South Lebanon Army militia could be incorporated into the Lebanese army.
But he scorns the idea that Israeli withdrawal would put an end to Hizbollah's military aggression. Israel's presence has nothing to do with the support for Hizbollah, he says. There is 'no antagonism' to Israel's presence inside its 'security zone'. Hizbollah's attacks on Israel are only a pretext for the group's Iranian backers to justify their presence in Lebanon. The Syrians help because they are afraid to upset Iran. 'The real intention is to set up an Islamic republic in Lebanon. If we withdraw now there will be an Islamic state in south Lebanon.'
Israel's prerequisite for withdrawal is not only destruction of Hizbollah but Syrian withdrawal from Lebanese land. 'I have always believed in symmetry in Lebanon. As long as the Syrians have forces and allies there, we have forces and allies there,' says Mr Sneh.
While positions on either side harden, all the evidence is that Hizbollah are getting better at 'resisting' the Israeli presence, and that Israel is preparing tougher measures to counter this. Southern Lebanon looks certain to become an increasingly bloody 'side-show' to the peace talks - until and unless it suits Syria and Israel to cut a deal over the Golan Heights.Reuse content