Among the many recent attempts to demonstrate the medical benefits of religious activity, the methodologically strongest seem to be studies of the effects of distant intercessory prayer (IP). In these studies, patients are randomly assigned to receive standard care or standard care plus the prayers or "healing intentions" of distant intercessors. Most of the scientific community has dismissed such research, but cavalier rejection of studies of IP is unwise, because IP studies appear to conform to the standards of randomized controlled trials (RCTs) and, as such, would have a significant advantage over observational investigations of associations between religious variables and health outcomes. As we demonstrate, however, studies of IP fail to meet the standards of RCTs in several critical respects. They fail to adequately measure and control exposure to prayer from others, which is likely to exceed IP and to vary widely from subject to subject, and whose magnitude is unknown. This supplemental prayer so greatly attenuates the differences between the treatment and control groups that sample sizes are too large to justify studies of IP. Further, IP studies generally do not specify the outcome variables, raising problems of multiple comparisons and Type 1 errors. Finally, these studies claim findings incompatible with current views of the physical universe and consciousness. Unless these problems are solved, studies of IP should not be conducted.