A strong majority of Israelis want Prime Minister Ehud Olmert to resign, four new polls have found. But one of them shows a falloff in that demand in the nine months between the publication of the interim Winograd Report on the Second Lebanon War last April and the final report on Wednesday. A Teleseker poll, broadcast on Army Radio and published in Ma'ariv, found 57 percent said Olmert should resign, compared to 73% after the committee's interim report was published. Some 33% said he should stay, compared to 17% after the interim report came out. Forty-two percent of those polled preferred Olmert's government to stay in power until the end of its term (November 2010) or an earlier date agreed upon in advance. However, 27% thought new elections should be held as soon as possible. Additionally, 39% of respondents said that if Olmert didn't resign, Labor leader and Defense Minister Ehud Barak should pull his party out of the government and bring about early elections. A total of 22% said Barak should remain in Olmert's coalition and a similar number thought Barak should remain in the coalition but only after setting a date for new elections in approximately a year. The poll also checked respondents' views of MKs seeking to topple Olmert and take his place, and found Likud leader Binyamin Netanyahu leading, with 37.4% saying he is a suitable candidate for prime minister. Foreign Minister Tzipi Livni, of Olmert's Kadima Party, enjoys 20.9% of the public's support, with Barak closely trailing her with 19%. The survey did not cite the number of respondents, their socioeconomic background or a margin of error. A survey by the Maagar Mohot agency found 60% of Israelis thought Olmert should resign, while only 19% thought he should not step down. The poll questioned 474 Israelis immediately after Wednesday's publication of the report and had a margin of error of 4.5 percentage points. Another poll, commissioned by Israel Radio and conducted by Shvakim Panorama, found that the public's trust in the Winograd Committee dropped from 73% before the final report was published to 68.8% immediately after it was made public. Israel Radio's poll also showed that 44.4% wanted Olmert to resign and to hold general elections within 6-12 months, but only 21.7% thought he should resign immediately and be replaced by someone from within Kadima ranks. On the other hand, 31.6% thought Olmert should remain in office. As for Barak, 33.7% of respondents said he should not leave his position as defense minister, take Labor out of the coalition and topple the government, while a similar 32.2% said he should quit immediately. The same poll found that 37.8% thought Livni should assist Olmert in staying in office, while 34.9% thought she should resign immediately and work to topple his government. A Yisrael Hayom/Gal Hadash (New Wave Research) poll found 57% of respondents believed Olmert should step down, 25% said he shouldn't, and 18% did not have an opinion. Some 65% said if Olmert decided to quit, Israel should go to elections now, while 23% said he should be replaced with someone else from Kadima, and 12% said they didn't know. Some 80% of those polled said that despite the Winograd Report, they still trusted the army, 15% said they didn't, and 5% didn't know. AP contributed to this report.