UK Prime Minister Tony Blair has made it clear that commitment to getting rid of Iraqi President Saddam Hussein should be accompanied by a commitment to ending the Israeli-Palestinian conflict.
In the case of the second, Mr Blair is betting on the so-called "road map" - a staged peace plan drawn up by international mediators.
Mr Sharon cannot be forced into an agreement
It is expected to be published once the new Palestinian Prime Minister, Mahmoud Abbas, presents his cabinet.
The Israeli Government is watching closely.
Prime Minister Ariel Sharon - normally keen to play the centurion - has been asked to take on the role of mute spear-carrier in the Iraq war. That gives him plenty of time to work on his diplomatic strategy.
That means fending off international pressure to swallow whole the road map - which is basically a collection of recent unsuccessful peace plans bolted together along with a timetable for a Palestinian state.
Mr Sharon does not much like the plan as it stands, but he knows he cannot just dismiss it out of hand.
"One of the things that Ariel Sharon has learned is that you can't beat something with nothing," says Gerald Steinberg, the director of the political studies department at Bar Ilan University.
"Israel has to put something on the table - it can't just say no. Something else has to be offered."
That something may be an Israeli plan. Sources say a plan is being drawn up by Mr Sharon's advisors and that it calls for some sort of Palestinian mini-state.
It is not the sort of plan the road map navigators have in mind. They want Washington to put its full weight on Mr Sharon to fall into line.
Israelis know what that might involve.
"There are many ways that President Bush might use to pressure Israel and Sharon - through assistance, the lease of technology," says Dani Yatom, a former head of the Israeli intelligence agency Mossad.
"It is the way we will get backing from the US in the global political arena. And the way the Arab side will be treated."
But many here believe that in the end, the Bush administration will not pull the plug or do the pushing. They believe the diplomatic legwork will be left to Tony Blair.
"Britain has very little leverage," says Professor Steinberg, "Relations are very poor now.
"Israel is a democracy. In terms of forcing down a plan that Israelis don't think that'll work, it won't happen.
"There are already shelves of peace plans - another one won't make much difference."
That would not be good news for Tony Blair. His government's assumption is that overwhelming international pressure - following of a successful war in Iraq - will mean that both Israelis and Palestinians have to accept compromise and go along with the road map.
But, in this conflict and in this region, fundamental assumptions are often lost along the way.