This paper addresses the problem of how to place students in a sequence of hierarchically related courses from an (empirical) Bayesian point of view. Based on a minimal set of assumptions, it is shown that optimal mastery rules for the courses are always monotone and a nonincreasing function of the scores on the placement test. On the other hand, placement rules are not generally monotone but have a form depending on the specific shape of the probability distributions and utility functions in force. The results are further explored for a class of linear utility functions. Numerous illustrations and tables present data and statistical analysis. (Contains 20 references.) (Author/TS)