Unlike the presidential candidates who have three debates in which to show their strengths in a head-to-head battle, the vice presidential candidates only have one, and it's this Tuesday night at Case Western University in Cleveland, Ohio. 

With just 90 minutes to confront one another and convince voters of their relative superiority, Vice President Dick Cheney (search) and North Carolina Sen. John Edwards (search) have spent the weekend preparing in locations nearly as far away from one another as they can get.

Cheney has been at his Wyoming home, where's he's spent the past several weekends. Edwards has been in Chautauqua, N.Y. The two have been going over an array of policy questions that include both domestic and foreign issues.

Democrats often criticize Cheney for being too closely tied to his former company, Halliburton (search), which received lucrative rebuilding contracts in Iraq. Bush-Cheney strategists said Sunday that tactic won't work in Tuesday's debate.

"These sidebar issues in which Democrats have sidebar attacks won't have the currency with the American people. Cheney will defend positions, but he's not going to allow political attacks by Democrats to divert us from the issues of today," White House Communications Director Dan Bartlett told FOX News Sunday. 

Republicans often try to criticize Edwards for his work as a trial lawyer, but Democratic campaign strategists say that experience is likely to help the senator in the debate.

"I think if you look at Senator Edwards' past ... and the skills that he brings to the table of holding people accountable, powerful people who don't want to tell the truth and don't want to tell the public what they know and what they've done, I think they will serve him well," said senior Kerry adviser Joe Lockhart. 

Edwards is heading to Cleveland on Monday after doing a couple run-throughs on a mock set complete with cameras, a moderator and a small audience to simulate the debate venue. The senator's wife, Elizabeth, and senior staffers are helping him prepare.

In his practice debates, D.C. lawyer Bob Barnett (search) is playing the role of Dick Cheney, as he did four years ago for Sen. Joe Lieberman. Barnett was one of the lawyers who defended former President Bill Clinton during the impeachment hearings. He also has helped other Democratic candidates, including Michael Dukakis and Geraldine Ferraro, prepare for their debate matchups. Both faced former President George H.W. Bush in the 1980s.

Over the weekend, Cheney's daughter Liz and adviser Mary Matalin worked closely with him on debate preparations. Ohio Rep. Rob Portman (search) was standing in as Edwards for Cheney's practice debates. Aides say the vice president will take some time off on Monday from the formal practice session and spend the time relaxing and collecting his thoughts. He will travel to Cleveland on Tuesday. 

A coin toss determined that Cheney will answer the first question and Edwards will go first in closing remarks. The candidates will sit at a table facing moderator Gwen Ifill of PBS. The candidates have not yet agreed on whether to use the timing lights that were present in the first presidential debate. 

FOX News' Molly Henneberg contributed to this report.