From an Israeli perspective, the three key elements were isolating Iran, coaxing moderate Arab countries into moving toward normalization with Israel and getting oil-rich Arab states to honor their financial pledges to the Palestinians.
Progress on all or some of these issues would significantly boost Israeli foreign policy goals.
On Iran, Bush's rhetoric was uncompromising. In a major policy statement in Abu Dhabi, he described Tehran as a threat to world peace and called on America's allies to join the United States in confronting the danger "before it was too late."
Bush accused the Iranian regime of funding terrorists and extremists, undermining peace in Lebanon, sending arms to the Taliban, seeking to intimidate its neighbors with alarming rhetoric, defying the United Nations and destabilizing the entire region by refusing to be open about its nuclear program.
But after last month's National Intelligence Estimate (NIE), which concluded that Iran had suspended a clandestine nuclear weapons program in 2003, it is unclear what action the United States intends to take.
Bush's post-NIE Mideast diplomacy can be read in two different ways: bolstering the moderate Arab coalition against Iran as part of an ongoing policy of containment through diplomatic and economic sanctions, or as laying the diplomatic groundwork for a possible military strike against Iranian nuclear installations before the president leaves office.
Israeli experts are divided over how far Bush is likely to go.
Eitan Gilboa of Bar-Ilan University's BESA Center for Strategic Studies said he would be very surprised if Bush does anything dramatic during the remainder of his term, such as initiating a dialogue with the ayatollahs or launching a military strike.
Indeed, Gilboa said the president may have ordered the NIE findings to get himself off the hook on attacking Iran.
"The administration has no stomach for military action now," Gilboa said. "The public doesn't want it, and it could hurt the chances of the Republican candidate in the November presidential election."
But Roni Bart, an expert on U.S. Middle East policy at Tel Aviv University's Institute for National Security Studies, argues that the NIE has been far less influential than is generally thought and that Bush still may attack Iran if he believes it is the right thing to do.
Bart points out that the NIE failed to convince the Europeans, the Arab states, the U.S. presidential candidates and, most important, Bush himself that the Iranians have abandoned their drive toward nuclear weapons.
"After seven years we know a bit about Bush. He doesn't care about public opinion, and he says God talks to him," Bart said. "If he thought he should attack before the NIE, and if that's what he still thinks a few months from now, the NIE won't change his mind."
Bush is committed to beefing up moderate forces in the Persian Gulf region as part of the effort to contain Iran. Most significant, the United States intends to supply Saudi Arabia with $20 billion in state-of-the-art weaponry over the coming decade.
Nevertheless, the moderate Arab states are highly ambivalent about war with Iran. Both Kuwait and the United Arab Emirates told Bush they would not allow U.S. forces to use their territory as a launching pad for a military strike.
As for normalization between Israel and the Arab world, Bush declared in Jerusalem last week that the Arab states should "reach out to Israel," describing it as a step "that was long overdue" and that would give Israel the confidence to make concessions to the Palestinians.
Indeed, Israel argues that things would proceed much better if the Arabs make a reciprocal gesture of normalization toward Israel for each step Israel makes toward the Palestinians. The Arabs, however, see normalization as a prize that Israel will be entitled to only after a peace treaty with the Palestinians is complete.
So far, the Arabs have shown little sign of any change in this attitude.
The smattering of Israeli dealings in the Gulf countries is kept highly secret for fear of embarrassing Arab host countries. Last year, when a Kenyan athlete running for Bahrain won the marathon in Tiberias, the Gulf state summarily revoked his Bahraini citizenship for competing in Israel.
Last week, though, offered a significant exception to the rule: The Saudi-owned newspaper A-Sharq Al-Awsat ran an article calling on the Arabs to show greater understanding for Israeli concerns.
Written by Mamoun Fandy, an Egyptian-born scholar at the International Institute of Strategic Studies in London, the column urged the Arabs to do much more to convince the West they really want peace and stability -- including peace with Israel.
"Perhaps the time has come for the Arabs, particularly the Palestinians, to take a serious view of Israel's strategic fears," Fandy wrote. "The Israeli question about the nature of the Palestinian state is logical and legitimate. Will this state add to stability or instability in the region?"
The fact that such views were allowed to appear in a publication connected to the Saudi royal house constituted a small but possibly significant crack in the rejectionists' wall.
Bush on his trip also sought to ensure that the Arab contribution to the $7.4 billion aid package raised for the Palestinians at last month's donor conference in Paris comes through. The largest pledge was $500 million from the Saudis over the next three years.
Israel has a clear interest in the money getting to the Palestinian Authority in the West Bank. Israeli policy is based on sustaining the growing contrast between an increasingly prosperous West Bank and an economically declining Gaza Strip. The hope is that this will help bring down Hamas in Gaza and create a large Palestinian majority for peace.
Annapolis, Paris and Bush's current Middle East tour are all part of this grand peacemaking scheme. But will it be enough in a region teeming with so many powerful countervailing forces?
Leslie Susser is diplomatic correspondent for the Jerusalem Report.