By extending their arm to attack a Palestinian camp near Damascus, the Israelis might also be hoping to prise open the file on US President George W Bush's desk marked "Syria".
Syria has for long been a rhetorical target of hawks in Washington, but it has been lying low recently. President Bashar al-Assad has hinted that economic and other reforms are on the way. Syria says it has closed offices used by Palestinian groups.
But Israel wants to keep the Syrian issue alive in US minds.
Israel wants to keep Syria top of the US agenda
"Israel has successfully put Syria on the agenda of the neo-conservatives in Washington and wants to keep it there. Vice-President [Dick] Cheney and Defence Secretary [Donald] Rumsfeld are gunning for Syria. It is a huge move in this conflict," Hania Farhan, Middle East director of the Economist Intelligence Unit in London, told BBC News Online.
Israel will already have been pleased by the statement by the US Ambassador to the UN John Negroponte that "Syria is on the wrong side of the war on terrorism".
The attack means that Israel has all but given up on the so-called roadmap to Middle East peace, which now lies trampled on the floor.
The roadmap has gone the way of the Oslo agreement, which also withered under the impact of suicide bombs.
The prospect now is the long haul of a "low intensity" war, but which could from time to time take on the features of major conflict.
In such a campaign, it is important for Israel to have the United States by its side.
By attacking a target in Syria, Israel might be in tune with Mr Bush's continuing militant mood.
The president is reported by the Washington Post to have told King Abdullah of Jordan recently: "I'm still in a war mode and the war is terrorism."
Mr Sharon's instincts
Israeli Prime Minister Ariel Sharon's own instincts are to take the fight to his enemies.
He did this in 1953 when, as commander of special operations Unit 101, he went into Jordan to attack Palestinian guerrillas.
In the 1973 war, he unexpectedly crossed the Suez Canal and threatened the Egyptians with encirclement.
In 1982, he took Israeli troops to Beirut.
It may be that Syria can avoid being drawn in too deeply.
Over the past 30 years, since the Yom Kippur War exactly 30 years this day, it has kept its border with Israel on the Golan Heights relatively quiet and has acted through its allies in Lebanon instead.
Certainly, its room for military manoeuvre is limited.
"Syria has no way of retaliating given its military weakness against Israel. That's why Israel knew it would get away with this," Ms Farhan said.
"I don't think that Syria thought it would come to this, that it would be attacked directly."
The Syrian connection
The stated Israeli reason for the attack, that it targeted a "training camp used by terrorist organisations, where operatives of Hamas and the Islamic Jihad train while enjoying the backing of Syria" must also be taken seriously.
The Israelis have often accused Syria of harbouring a number of militant Palestinian groups. These traditionally included the Popular Front for the Liberation of Palestine which is less active these days.
More recently, Israel has said that Hamas and Islamic Jihad have used Syria as a base for planning and organisation.
The Israelis released a video of what they said was the camp they attacked at Ein Saheb. This showed a large amount of military equipment in a cave. The video seems to have been obtained off Iranian TV though its origin remains unexplained.
Syria has maintained that these groups are engaged in resistance not terrorism and that it has not helped them to any significant degree.
The Arafat factor
Another reason for the raid could well have been the need to reduce the pressure on the government to carry out its threat to "remove" Yasser Arafat.
Many in Mr Sharon's own cabinet are calling for Mr Arafat's expulsion. Some voices in Israel (the Jerusalem Post for one) have even called for his assassination.
By attacking a target inside Syria for the first time in decades, Mr Sharon might feel that he has satisfied a desire among political and public opinion for action. For now.
Iran in spotlight
And Syria is not the only country mentioned in the statement from the Israeli military. Iran was named twice.
"The Islamic Jihad," the statement said, "enjoys the support and backing of countries in the region, foremost among them Iran and Syria."
It accused Iran of providing "funding and direction".
It is perhaps no coincidence that Iran is currently the Middle Eastern country getting most critical American attention with the arguments over its development of a nuclear capability.