In the debate with Vice President Cheney on Tuesday, Sen. John Edwards referred to allegations of wrongdoing by Halliburton Corp. several times and raised questions about the Bush administration's handling of government contracting in Iraq.

But in doing so, Edwards occasionally jumbled or oversimplified the complex details of the company's role as a contractor and of its ties to Cheney, who served as Halliburton's chief executive from 1995 to 2000.

Cheney, for his part, said the Democrats "know the charges are false," even though some are the subject of ongoing investigations.

Edwards correctly noted that Halliburton secured a $7.5 billion no-bid contract from the Pentagon shortly before the war in Iraq to repair any damage to the country's oil fields. He also accurately said that the government is contemplating withholding money from Halliburton because some auditors believe the company has not properly accounted for its bills in Iraq.

But the Democrat conflated two contracts, the second of which is a troop support arrangement awarded to Halliburton before the war, after a competition. That contract helped make Halliburton the top government contractor in Iraq. The Pentagon has considered -- but has not acted on -- several suggestions from auditors to withhold 15 percent of future payments because of questions about the company's billing.

Edwards also chided Cheney for allowing Halliburton to do business in Iran and for pressing U.S. officials for the right to do business in Iran while he was Halliburton's chief executive.

Edwards was referring to oil service work performed in Iran by a Cayman Islands subsidiary called Halliburton Products & Services Ltd. The Houston-based parent company disclosed this summer that a three-year Treasury Department investigation -- into whether that arrangement was a violation of national security sanctions that prohibit U.S. companies from doing business in Iran -- had escalated into a criminal investigation by the Justice Department.

Halliburton has said repeatedly in documents on file with the government that its subsidiary operated legally in Iran, outside the control of U.S. executives.

At one point, Edwards compared Halliburton during Cheney's tenure as chief executive to Enron Corp., the energy trading giant involved in one of the nation's biggest accounting frauds. "While he was CEO of Halliburton, they paid millions of dollars in fines for providing false information on their company, just like Enron," Edwards said.

Here Edwards appeared to be referring to the company's agreement in August to pay $7.5 million to settle Securities and Exchange Commission charges that it failed to disclose a change in accounting practices that allowed the company to report higher earnings in 1998 and 1999, while Cheney was still chief executive. The SEC also cited Halliburton for "unacceptable lapses" that hindered investigators. Cheney, who was not charged with wrongdoing, fully cooperated with investigators, the SEC said.

In one striking line during the debate, Edwards said that Halliburton is "now under investigation for having bribed foreign officials." Halliburton subsidiary KBR is under investigation by the Justice Department over allegations that former employees bribed Nigerian officials to secure work on a huge gas liquefaction plant there. The SEC is also investigating. But the company contends that the alleged wrongdoing occurred before the Cheney-led Halliburton acquired a subsidiary that was involved in the Nigerian deal.

In response to Edwards's remarks, the vice president offered few specifics but asserted that "there is no substance to the charges."

At one point in the debate, Sen. John Edwards compared Halliburton Corp., during Dick Cheney's tenure as chief executive, to the disgraced Enron Corp.