  Several experiments [1-3] show significant deviations from predictions of the
statistical model of nuclear reactions. We summarize unsuccessful recent
theoretical efforts to account for such disagreement in terms of a violation of
orthogonal invariance caused by the Thomas-Ehrman shift. We report on numerical
simulations involving a large number of gamma decay channels that also give
rise to violation of orthogonal invariance but likewise do not account for the
discrepancies. We discuss the statistical model in the light of these results.
