WASHINGTON, July 4 (AP) -- American voters are about evenly divided on whether they think George W. Bush or Al Gore is the more honest candidate, but their desire for a president who tells the truth is growing, an Associated Press poll shows. Four in 10 voters picked honesty ahead of such traits as caring about people like them, showing strong leadership, standing up for beliefs and having a vision. In a November AP poll, one-third picked honesty, which ranked first then as well. The Monica Lewinsky affair and the long Clinton impeachment process sent the message to voters that "you can't believe what politicians are saying," said political scientist Merle Black of Emory University in Atlanta. "Now they want someone to tell it like it is." In the latest poll, conducted for the AP by ICR of Media, Pa., about a third picked Bush as most honest and a third picked Gore. Another third said neither candidate or they didn't know. The earlier poll, taken before the presidential primaries, did not ask people to compare the candidates on honesty. In the latest poll, black voters put the most emphasis on a candidate who cares about people like them, but honesty ranked second. When Bill Clinton ran for president in 1992, voters placed honesty near the top of the list of most important characteristics along with leadership abilities and the candidate's stand on issues. But in the new poll, honesty, at 39 percent, was far in front. Second was caring about people like you, at 17 percent, and then leadership at 14 percent. When registered voters in the new poll talked about the candidates, their comments quickly turned to who they did or did not trust. "I like Bush's character, his demeanor, his father," said Harry Auel, 49 and a salesman from Batavia, Ohio, who said he ``leans Republican." "Gore's been a little bit tainted by Clinton as far as I can tell." Tammy Lausch, a 28-year-old daycare provider and mother of three, said Gore is more honest. "I don't trust Bush, with his dad being the president before," said Lausch, a Democrat from Colorado Springs, Colo. "I didn't like his dad, didn't trust him either, his background was CIA. There are a lot of secrets there." The poll showed the overall race close, 40 percent for Bush and 39 percent for Gore, among registered voters. The telephone poll of 798 registered voters was taken June 21-25. It has an error margin of plus or minus 4 percentage points. Other recent polls of registered voters have shown the race close, too, but polls that measured only likely voters have given Bush an advantage. Bush, the Republican governor of Texas, was favored on strong leadership skills, 49 percent to 32 percent, and as a candidate who stands up for what he believes, 44 percent to 38 percent. Gore, the Democratic vice president, was seen by more voters as caring about people like them, 44 percent to 34 percent, and as a candidate with a vision for the future, 46 percent to 37 percent. "I feel Bush has good leadership qualities," said Kimberly Jamison, a middle-school teacher who is registered Democratic for local politics but leans Republican in national races. "Bush seems to be able to handle the press well, he doesn't seem to be goaded into answering something too quickly. I like somebody who thinks through their decisions." Brendan Klein, a 51-year-old commercial-building painter from Minneapolis, said he doesn't want another Bush in the White House. "I've had enough of the Bushes with his dad," said Klein, who leans Democratic. "I about starved to death under the trickle-down theories. For the first time in how many years, the little guy has some money in his pocket."