The federal judge who oversaw the trial of five associates of imprisoned swindler Bernard Madoff refused to overturn their convictions for helping their former boss run one of the world's biggest Ponzi schemes.

U.S. District Judge Laura Taylor Swain said on Thursday there was sufficient evidence for jurors to have convicted back-office director Daniel Bonventre, portfolio managers Annette Bongiorno and Joann Crupi, and computer programmers Jerome O'Hara and George Perez on all counts they faced, including securities fraud and conspiracy to defraud.

Swain also rejected the defendants' alternative argument that they deserved a new trial because prosecutors made improper remarks during their opening and closing statements.

The defendants were convicted on March 24, and are scheduled to be sentenced in mid-September.