In many societies legislators try to reduce the number of criminal acts, especially acts of violence, by laws requiring assessment and prediction of the dangerousness of individuals known for criminal violence. This paper discusses the problems of predicting criminal violence by mentally ill persons. After elaborating the intricate theoretical and methodological difficulties facing any variant of behavior prediction, the author goes on to explain why it is so difficult to compare the predictive power of several prediction instruments. Such a comparison is essential for any attempt to determine the most powerful instrument for particular groups of subjects. In the second part the paper documents and discusses the power of several new instruments (VRAG, HCR-20, PCL-R, for instance) for predicting violence by mentally ill patients. Although the results achieved by using these instruments are in most cases better than mere chance, they leave a lot of serious questions open because even the better instruments are affected by the problem of combining moderate sensitivity with an intolerable rate of false positives or a high rate of negative prediction with an intolerable low positive prediction rate.