TORONTO - Conrad Black's remaining convictions should be dropped because the prosecution's case is "feeble" now that the U.S. Supreme Court has narrowed the scope of the law used to convict him, the former media mogul's lawyers say.

Last month the court set aside Black's convictions for so-called "honest services fraud" -- a concept developed in the 1970s to convict corrupt politicians -- because honest services fraud is limited to bribes or kickbacks, neither of which Black was accused of.

It's very likely at least one of the jurors in Black's trial used the concept of honest services fraud to justify Black's other convictions for fraud and obstruction of justice, defence lawyer Miguel Estrada argued in a filing submitted to the U.S. Court of Appeals late Monday.

"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," the documents say.

And the obstruction of justice charge is irrelevant if all the other charges against Black are thrown out, they add.

"The government cannot now establish beyond a reasonable doubt that the jury would have credited the government's feeble showings on those issues if it had been aware that the underlying fraud offence it most likely found -- 'honest services' -- was not a crime at all," the documents say.

"Because the government cannot meet its burden, this court should now reverse each of the four counts of conviction that survived the jury's sweeping rejection of the government's theft theories," they add.

The defence's filing also apply to the remaining convictions against co-defendants Peter Atkinson, John Boultbee and Mark Kipnis.

The prosecution's filings were not yet available on the U.S. Court of Appeals website, and a spokesman did not immediately return calls for comment Monday night.

However, Bloomberg reported the prosecution maintained that Black's remaining convictions should be upheld.

A panel of three judges at the U.S. appeals court is examining how to proceed with Black's case following the Supreme Court's decision last month.

Montreal-born Black, who was forced to renounce his Canadian citizenship in 2001 in order to accept an invitation to join the British House of Lords as Lord Black of Crossharbour, is currently free on bail after serving more than two years in a Florida prison.

Black recently dropped his request to return to Canada and will remain in the Unites States while the appeal that could bring a final resolution to his case goes ahead.

Monday's submissions will be reviewed by a panel of three appellate circuit judges led by Judge Richard Posner, who presided over Black's last appeal and took only 20 days to reach a decision.

Black is expected to return to a Chicago court on Sept. 20 for a bail update, where he could make a request to return to Canada again.

He is still facing several civil suits, including a $71-million lawsuit by the U.S. Internal Revenue Service for alleged unpaid taxes, which he has challenged.

The convictions were in relation to US$5.5 million in payments that Black, Kipnis and Boultbee received from a subsidiary of the Hollinger media chain, which Black founded.

U.S. prosecutors alleged Black and three other executives orchestrated a scheme to pocket about $60 million in non-compete payments negotiated with buyers when Hollinger sold newspaper assets -- money that should have gone to shareholders.

The so-called "non-compete payments" -- stemming from the sale of Canadian papers to the former Canwest and U.S. papers to several U.S. buyers in 2000-- were at the heart of the government's case.

Hollinger once owned the Chicago Sun-Times, The Daily Telegraph of London, The Jerusalem Post and hundreds of community papers in the U.S. and Canada.