A federal judge in Denver will begin deciding the issue Thursday when Mr. McVeigh's new lawyers appear in court in the last round of appeals of his conviction and death sentence for the 1995 Oklahoma City bombing.
Mr. McVeigh's appellate team hopes to persuade U.S. District Judge Richard Matsch to order more extensive hearings so that it can present evidence of alleged misconduct by former defense counsel Stephen Jones of Enid, Okla.
Lead attorney Dennis Hartley of Colorado Springs, Colo., also has alleged in court documents that prosecutors improperly hid evidence favorable to the defense and that federal agents "irrevocably" tainted the jury pool by assuring "maximum national publicity" of Mr. McVeigh's arrest.
Mr. Jones was confident that he would be vindicated by the court if the matter were to be explored fully.
"I have no apologies to make for our defense or the strategy or the time or effort we put into it," he said this week in a telephone interview.
Special Assistant U.S. Attorney Sean Connelly could not be reached for comment. He has previously said that he believes Mr. McVeigh received a fair trial that protected his constitutional rights.
Thursday's oral arguments mark an early stage in Mr. McVeigh's second, and presumably final, appeal of his conviction for masterminding the daring workday attack that killed 168 people and injured more than 500.
"This is it," said Denver attorney Andrew Cohen, who covered Mr. McVeigh's trial for CBS Radio. "Once he goes to this level, and perhaps gets the opportunity to at least try to get the Supreme Court involved, there is very little else he can do.
"The system in the past few years has been streamlined significantly to reduce the number of appeals and the time between appeals."
Mr. McVeigh, a 32-year-old Gulf War veteran, is not expected to attend Thursday's proceeding. He is awaiting execution on federal death row near Terre Haute, Ind.
Federal prosecutors say he bombed the Alfred P. Murrah Federal Building on April 19, 1995, in retaliation for what he perceived as the government's mishandling of the deadly 51-day siege at the Branch Davidian compound near Waco in 1993.
The oral arguments before Judge Matsch will unfold in his Denver courtroom, just across the street from where he presided over Mr. McVeigh's trial. Judge Matsch ordered the case moved to Denver because of extensive pre-trial publicity in Oklahoma City.
Mr. McVeigh's first round of appeals was unsuccessful. The 10th U.S. Circuit Court of Appeals in Denver rejected arguments that his trial was tainted by jury misconduct and news reports that he had confessed to the crime. The U.S. Supreme Court later refused to hear the case.
His latest bid for a new trial may be even more daunting, legal experts said, because of the high standards that must be met to prove ineffective assistance of counsel.
Mr. McVeigh's new appeal is based primarily on allegations that Mr. Jones engaged in a "dangerous dalliance" with the news media that resulted in the leaking of inflammatory information to The Dallas Morning News, The New York Times, ABC News and Playboy magazine.
"Stephen Jones' representation of Timothy McVeigh was burdened by intolerable conflicts of interest that prevented complete and dedicated commitment to the client," Mr. Hartley wrote in a 66-page appeal filed March 6.
"Jones' representation was driven not to advance the interests of McVeigh, but to advance his own financial, literary, political and personal interests."
Mr. McVeigh's appeal claims he warned Mr. Jones about his lawyer's relationship with the news media and said it detracted from his work on the case.
"I am afraid you are becoming addicted to the 'media bug,'" the appeal quoted Mr. McVeigh as saying. "Every time I turn around you are doing another TV, newspaper or radio interview.
"Please resist the lure and temptation of the camera."
Mr. Hartley also accused Mr. Jones of violating bar association rules by signing a book contract in June 1997 while he still represented Mr. McVeigh. Mr. Jones later changed publishers and wrote Others Unknown: The Oklahoma City Bombing Case and Conspiracy, published in 1998.
Mr. Jones denied signing any contact until months after he quit the case at Mr. McVeigh's insistence. He expressed reluctance to testify against his former client, but said he would do so if Judge Matsch wanted to fully explore the issue of ineffective assistance of counsel.
"None of those points have any legal merit," he said, "and a substantial number of them are factually inaccurate."
Mr. Jones said he believes he gave Mr. McVeigh "a zealous defense, an aggressive defense. Everything that could be done for him was done. He got a change of venue. We got a different judge. He got a separate trial. He got money for an adequate defense. We conducted a thorough investigation. Some of the damaging evidence the government had was kept out on our motion.
"Under those circumstances, you simply cannot say he had an ineffective assistance of counsel. It simply doesn't meet the standard."
In court documents made public Wednesday, Mr. McVeigh's appellate team dropped six ineffective-assistance-of-counsel claims, including an allegation that defense lawyers did not object soon enough to the often emotional testimony of those who survived or who lost loved ones in the blast.
Other complaints withdrawn included that trial attorneys inadequately challenged evidence of explosive residue on Mr. McVeigh; mounted a "feeble effort" to introduce a report critical of the FBI laboratory; and relied too much on "inadmissible evidence and the lack of a viable theory of defense."
One of Mr. McVeigh's Army buddies, Terry Nichols, was convicted in a separate federal trial of conspiracy and manslaughter but was acquitted of murdering eight federal law enforcement officers who died in the blast. He was sentenced to life in federal prison.