This report considers a university faculty which is divided into k grades. The total size is to remain fixed, but the proportions in the grades may vary. The problem is to find control strategies which will bring about desired changes in these proportions. This report is confined to investigating what can be achieved by controlling the numbers of new appointments made into each grade. It is assumed that movements within the system and to the outside would be governed by time-homogeneous transition probabilities. A number of theorems are presented showing that not all structures can be attained and that some which are attainable cannot be maintained. Some bounds are given for the length of time needed to achieve the goal when this is possible. A number of suboptimal strategies are proposed and their performance is studied empirically. Suggestions are made for further research. Finally, a nontechnical summary of this analysis is given at the beginning of this report. (Author)