The backing Prime Minister Ehud Olmert received from some of his ministers Sunday was downright collegial, even from some of those who view themselves as his rivals inside the Kadima Party. Transportation Minister Shaul Mofaz, a man who has never hidden his prime ministerial aspirations, said that Olmert, like everyone else in the country, enjoys the presumption of innocence. Interior Minister Meir Sheetrit, who has long had his eyes on the prime minister's seat, wished Olmert well in trying to clear his name and said the prime minister has proven in the past, especially the way he rode out the Winograd Committee storm, that he can function under pressure. Even Yitzhak Cohen of Shas, the party considered Olmert's weakest coalition link, said that at this point, Olmert could continue to serve as prime minister. And Defense Minister Ehud Barak didn't even wait until Sunday to throw his support to the beleaguered Olmert, saying last Monday that he hoped "for everyone's sake, and for Olmert's sake, that it turns out the suspicions that are circulating are baseless." The one minister whose voice has been noticeably absent in support of Olmert, and who has also not hinted that she either hopes or believes he will come out of the investigation still standing, is Foreign Minister Tzipi Livni. Indeed, the day before Barak's comment, a tense-looking Livni, standing next to visiting US Secretary of State Condoleezza Rice, said "The only right thing to do at this stage is to let those investigating and enforcing the law do their work." While saying that she had "full confidence" in the country's law enforcement apparatus, Livni glaringly refrained from saying she had full confidence in her boss. Livni is not Olmert's only rival - Barak, Mofaz and Sheetrit have all made clear that would like to unseat him. Yet only Livni has refused to throw him a public crumb of support. Why? The reason has to do with Livni's main - perhaps even only - real electoral asset: a perception of integrity. With the public scanning a field of what it increasingly views as corrupt politicians, she stands out - and wants to be perceived as standing out Ë†- as a flower among the thistles. In any election, either national or inside Kadima, this perceived integrity - not what she has achieved as a minister or accomplished as a politician - is her main asset. Mofaz and Barak beat Livni in spades when it comes to diplomatic and security experience and knowledge; Sheetrit can run circles around her as far as political savvy and experience is concerned. The card she holds is that she is perceived as honest and trustworthy, and coming to Olmert's defense would risk bending this card. There is also another, more prosaic, reason for her reticence to give Olmert any comfort at this time. Livni has the most to gain from a change in the guard now, because if Olmert is forced to step down if an indictment is served against him, she will take over - by virtue of her vice premier role - for a period of 100 days. And then the sky is the limit. Barak, Mofaz and Sheetrit, on the other hand, are in no rush for new elections now. Barak is in no hurry because his standing among the public still leaves a lot to be desired and he is waiting for that one victory - maybe in the South, maybe up North - that will enable him to regain national trust and popularity. Mofaz and Sheetrit, meanwhile, want to wait for elections because these two former Likud activists are busy doing what they used to do in the old party - signing people up to vote in the primaries. While they are getting old buddies to join Kadima for the primaries, Livni - for whom this type of work is anathema - is lagging far behind. A recent internal Kadima poll put Livni in seventh place among eligible Kadima voters, behind Olmert, Mofaz, Sheetrit, Dichter and even her deputy foreign minister Majallie Whbee. While Livni may be doing well in national polls, in surveys among Kadima primary voters she is getting clobbered. Political trench work is not Livni's forte, which is why she seems to prefer a quick Olmert exit. But while there are many imponderables in the whole Talansky affair, one thing can be said with almost perfect certainty - nothing about this affair is going to be quick.