After the U.S. Supreme Court eviscerated one of the fraud laws used to convict former media baron Conrad Black, federal prosecutors have to prove beyond a reasonable doubt that the trial error was harmless.

Lawyers for Black say the burden is impossible to meet and that a federal appeals court should toss out his conviction. Black was recently freed from prison after the Supreme Court in June ordered a review of his case because of flawed jury instructions.

The two sides laid out their positions in court papers due Monday at the federal appeals court in Chicago. The appellate court must decide whether to vacate Black’s 2007 fraud conviction.

Black and his co-defendants had challenged the constitutionality of the “honest-services” fraud law that makes it illegal “to deprive another of the intangible right of honest services.” Prosecutors had charged that the defendants had deprived shareholders by disguising money they stole from Hollinger International Inc., the former parent of the Chicago Sun-Times and other newspapers, as non-compete agreements tied to asset sales.

Prosecutors also charged Black and three former Hollinger executives with conventional money-and-property fraud. The jury was told they could convict the defendants under either fraud law without having to reveal which theory they chose. The jury convicted on three counts of fraud but acquitted on the bulk of the fraud charges. Black also was convicted of obstruction of justice.

The Supreme Court determined that prosecutors had broadly interpreted the honest-services statute and limited it to schemes involving bribes and kickbacks.

Since no such schemes were alleged against Black and his co-defendants, they could have been convicted for conduct that is not fraud.

Prosecutors, though, argued in court papers Monday that the honest-services liability was grounded in the theory that the defendants had stolen the company’s money, and not some alternative theory that even if the payments were legal the jury should still convict because they were not properly disclosed to shareholders.

Lawyers for Black and other defendants — Mark Kipnis, John Boultbee and Peter Atkinson — blasted the government’s argument.

“The government’s argument is factually baseless because before, during, and after trial the government made clear, consistently and repeatedly, that it was pursuing alternative theories of fraud, not a single ‘theft’ theory.”