Since the founding of the Society of Psychical Research in 1982, psychical researchers have, in each generation, generated research reports which they believed justified the existence of paranormal phenomena. Throughout this period the scientific establishment has either rejected or ignored such claims. The parapsychologists, with some justification, complained that their claims were being rejected without the benefit of a fair hearing. This paper asks the question of how well the best contemporary evidence for psi — the term used to designate ESP and psychokinetic phenomena — stands up to fair and unbiased appraisal. The results of the scrutiny of the three most widely heralded programs of research — the remote viewing experiments, the psi ganzfeld research, and the work with random number generators — indicates that parapsychological research falls short of the professed standards of the field. In particular, the available reports indicate that randomization is often inadequate, multiple statistical testing without adjustment for significance levels is prevalent, possibilities for sensory leakage are not uniformly prevented, errors in use of statistical tests are much too common, and documentation is typically inadequate. Although the responsible critic cannot argue that these observed departures from optimal experimental procedures have been the sole cause of the reported findings, it is reasonable to demand that the parapsychologists produce consistently significant findings from experiments that are methodologically adequate before their claims are taken seriously.