About one-third of Texas voters say they are unsure who they'll vote for in the general election or will support someone other than the major candidates, according to a new Texas statewide poll conducted by Leland Beatty.

The poll finds that Donald Trump Donald John TrumpUS reimposes UN sanctions on Iran amid increasing tensions Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally MORE leads Hillary Clinton Hillary Diane Rodham ClintonJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Momentum growing among Republicans for Supreme Court vote before Election Day Warning signs flash for Lindsey Graham in South Carolina MORE by about 7 points in the state. The presumptive GOP nominee garnered the support of 36.8 percent of respondents, while Clinton won the support of 29.7 percent. Only 2.6 percent of respondents support Libertarian presidential nominee Gary Johnson Gary Earl JohnsonWhat the numbers say about Trump's chances at reelection Presidential race tightens in Minnesota as Trump plows resources into state The Hill's Campaign Report: Biden condemns violence, blames Trump for fomenting it l Bitter Mass. primaries reach the end l Super PAC spending set to explode MORE.

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Thirty-one percent of people surveyed said they were either unsure or would support someone other than the two major parties' presumptive nominees and Johnson.

For undecided voters or those not supporting the three candidates listed, the honesty and integrity of the candidates ranked as the most important issue, followed by the economy and jobs.

Over half of respondents who identified as Republicans said they may vote for down-ballot candidates outside the party, and about 27 percent of Republicans said they may not vote for a Republican at the top of the ticket.

The poll was conducted among 998 respondents from June 13-14. The margin of error is 3.1 percentage points.

Clinton won the Texas Democratic primary over Bernie Sanders Bernie SandersNYT editorial board remembers Ginsburg: She 'will forever have two legacies' Two GOP governors urge Republicans to hold off on Supreme Court nominee Sanders knocks McConnell: He's going against Ginsburg's 'dying wishes' MORE by 32 points. Trump finished second in the GOP primary, trailing Texas Sen. Ted Cruz Rafael (Ted) Edward CruzVideo of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral Sunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Democrat on Graham video urging people to 'use my words against me': 'Done' MORE by 17 points.