Rule 606(b) and its common law antecedents are analyzed and compared with more restrictive local Federal rules that supplement and enhance the effects of Rule 606(b). The policy reasons for the restrictions placed on obtaining information concerning jury misconduct from the jurors themselves are examined, along with the suggestion that Rule 606(b) be reformulated to deal more directly with jury misconduct. The article concludes that the principles embodied in Rule 606(b) are valid and significant, for an exclusionary rule that frees the courts from dealing with new trial claims based on minor misconduct makes sense. However, the exclusionary rule embodied in Rule 606(b) should be reformulated to deal with false information and seriously improper influences upon jurors. A separate new uniform rule should govern jury investigation and new trials. 214 footnotes.