The former American football star's attorneys have filed a motion demanding a court hearing over whether law enforcement agencies have been secretly investigating the background and recent conduct of jurors.
Simpson's so-called "Dream Team" has demanded to know whether prosecutors were using the results of such investigations to persuade Judge Lance Ito, to disqualify unfavourable jurors because they fear their case is failing. If proved, the defence claims this would be grounds for the case to be dismissed.
The issue has come to the fore with the dismissal from the jury of Jeanette Harris, a 38-year-old black employment counsellor, for failing to disclose past experience of spousal abuse in a pre-trial jurors' questionnaire. After angrily leaving the courtroom, Mrs Harris gave a television interview in which she was overwhelmingly sympathetic to Simpson.