POTENTIAL JURORS WITH A PRIORI PROBABILITIES OF VOTING FOR CONVICTION ARE ASSUMED TO BE CHOSEN RANDOMLY FROM A POPULATION AND COME UP ONE AT A TIME FOR DECISION. EACH SIDE MUST DECIDE TO ACCEPT OR CHALLENGE A POTENTIAL JUROR AS A FUNCTION OF HIS A PRIORI PROBABILITY, THE DISTRIBUTION OF THESE PROBABILITIES IN THE POPULATION, THE NUMBER OF JURORS REMAINING TO BE SELECTED, AND THE NUMBER OF PEREMPTORIES BOTH SIDES HAVE REMAINING. A NUMBER OF CONCLUSIONS ARE DERIVED FROM THE NUMERICAL RESULTS HAVING TO DO WITH THE EFFECTS OF DIFFERENT NUMBERS AND PROPORTIONS OF CHALLENGES ALLOTTED TO EACH SIDE, DIFFERENT ASSUMED DISTRIBUTIONS FROM WHICH JURORS ARE CHOSEN, AND DIFFERENT SIZED JURIES. EMPIRICAL EVIDENCE, PARTICULARLY FROM RECENT, WIDELY PUBLICIZED TRIALS, IS PRESENTED IN SUPPORT OF THE MAJOR ASSUMPTIONS OF THE MODEL. DESPITE THE APPARENT APPLICABILITY OF THE MODEL TO SOME JURY SELECTION PROCEDURES, HOWEVER, IT IS ARGUED THAT PROCEDURES THAT ENCOURAGE STRATEGIC CALCULATIONS OF THE KIND MODELED INTRODUCE NOT ONLY AN EXTRANEOUS ELEMENT INTO THE JURY SELECTION PROCESS BUT MAY ALSO UNDERMINE A RIGHT OF THE ACCUSED GUARANTEED BY THE SIXTH AMENDMENT, AN IMPARTIAL JURY, THAT PREEMPTORY CHALLENGES ARE DESIGNED TO PROMOTE. (AUTHOR ABSTRACT)...MSP