Conrad Black's lawyer will enter a Chicago appeals court Wednesday, hoping to get fraud and obstruction of justice convictions against the former media mogul dropped.

Black is currently out on bail after serving two years in jail. His case hinges on a controversial law: the so-called "honest services" argument used to convict him.

The U.S. Supreme Court ruled in June that the "honest services" law is too vague, and narrowed its definition. When it was used to prosecute Black, the law could target corporate executives who had a conflict of interest in their business dealings.

But the Supreme Court removed that part of the law, so now a successful "honest services" fraud conviction rests on bribery or kickbacks, neither of which were involved in the Black case.

Hundreds of white-collar crime convictions have been called into question because of the Supreme Court ruling, but Black's case is the first to be heard in appeals court.

"It is a little bit, shall we say, sublime that someone from another country would overturn a U.S. law but that's the way it is," former prosecutor Terry Sullivan told CTV News.

Black has refused to accept his conviction, always declaring his innocence and vowing to clear his name since he was first sentenced in 2007. He spent 28 months behind bars before getting released on bail.

Chicago-based business trial lawyer Hugh Totten, who has closely followed the case, said Black is nothing if not persistent.

"Whether you like him or not, you have to admire his toughness and his tenacity in putting up with the weight of the federal government of the United States coming down on him year after year," he told CTV News.

Black's lawyer Miguel Estrada is expected to argue that his client's fraud and obstruction convictions are linked to the "honest services" law that has since been changed, and so the charges should be dropped.

""The government cannot possibly negate the likelihood that at least one juror took the shortest path to guilty verdicts by convicting for something less than fraud, i.e., honest-services fraud," Estrada wrote in a filing to the court.

Estrada will be arguing against U.S. attorney Patrick Fitzgerald, who led the first prosecution team against Black. In another written filing from Fitzgerald, he argued that the honest services argument was not essential to Black's conviction.

"What was not at issue (during the trial) is what the defendants argued after the trial, namely, that somehow the government sought to convict the defendants on an alternative honest-services theory," he wrote.