Olmert, the most unpopular and discredited prime minister in Israel's entire history, announced Wednesday he would resign in September as a corruption probe that could put him in court to face possible bribery charges crawls ever closer.

Olmert's resignation will allow his new centrist Kadima Party to hold primary elections to choose a new leader, who then will become prime minister. The relatively young, attractive and articulate Livni is the media favorite by far in both Israel and the United States. And she is also the favorite of U.S. Secretary of State Condoleezza Rice. But many Kadima Party members in Israel already think differently.

The Tel Aviv newspaper Yedioth Ahronoth, the most popular newspaper in Israel, reported Thursday that in a Dahaf Institute poll it had commissioned and published last Friday, Livni, while still the front-runner, was backed by only 38 percent of party members. Tough old right-leaning Mofaz, a former Israel Defense Forces chief of staff and defense minister who fought the Second Palestinian Intifada, ran unexpectedly close with 33 percent.

Olmert has been either prime minister or acting prime minister for two and a half years. He won an election in his own right after succeeding vastly popular and respected veteran Prime Minister Ariel Sharon when he was felled by a stroke in January 2006.

However, in July 2006, Olmert, his Defense Minister Amir Peretz, a trade union organizer with no military experience worth the name, and IDF Chief of Staff Lt. Gen. Dan Halutz, a former Israeli air force commander, launched a disastrously unsuccessful attempt to oust Hezbollah, the Iran- and Syria-backed Shiite Party of God in Southern Lebanon. Instead, Hezbollah stood its ground and was not ousted, and it was northern Israel that was bombarded with thousands of Katyusha multiple-rocket launch system warheads, though casualties were fortunately light.

The fiasco cost Peretz and Halutz their jobs, but Olmert has hung on for another two years, despite being totally discredited and a popularity rating down to single digits.

U.S. media reports have expressed concern about the future of the Annapolis peace process that Rice launched with enormous fanfare in November 2007. Olmert and Palestinian Authority President Mahmoud Abbas both came to Washington and Annapolis and solemnly pledged to work constructively together and make the process work. Livni hitched her star to it as well.

True believers in Annapolis are praying that Livni will win the Kadima primary -- which they take for granted -- and a subsequent Israeli election -- which they correctly realize they cannot take for granted -- and revive Annapolis.

In reality, there is nothing to revive, for the Annapolis process is as departed as Monty Python's famous dead parrot.

Abbas is as discredited a lame duck on the West Bank, where he tenuously clings to the illusion of power, as Olmert is in Israel. hamas, the formidable Islamic Resistance Movement, seized Gaza from him in 2007 and continues to hold it in an iron grip. Hamas has also quietly but implacably been extending its power beneath the surface in the West Bank, even though the United States, Israel and Jordan all have been desperately trying to prop up Abbas.

The vastly experienced Mofaz is already proving a far more formidable challenger to Livni than the pro-peace pundits in the Tel Aviv media or their American counterparts ever imagined. Whoever wins the Likud primary will then have to hold a general election in the next six months under Israel's ponderous constitution.

The opposition Likud Party is led by veteran leader Binyamin Netanyahu, a former prime minister, foreign minister and defense minister, and the Labor Party, Kadima's coalition partner in government, is led by Defense Minister Ehud Barak, who is also a former prime minister as well as a former IDF chief of staff and in his younger years the most successful commando leader in Israeli history.

Both Barak and Netanyahu were swept out of office by the Israeli public after unpopular and widely criticized terms as prime minister, but they both rehabilitated their reputations, Netanyahu as a tough but very successful finance minister under Sharon and Barak as a defense minister rebuilding the IDF after its humiliating Hezbollah war experience.

Livni, who has been a lackluster foreign minister, was also one of the country's top leaders during the 2006 mini-war fiasco, and that reputation could hurt her badly against heavy hitters Netanyahu and Barak.

As for Olmert, no one except the buddies he is accused of taking bribes from will miss him.