The authors are engaged in a project to produce a precise description of a design for a family of operating systems. The design decisions ue being expressed by means of formal module specifications. In an attempt to write a concise specification of one of the most critical modules, a "virtual memory mechanism," some previously discussed specification techniques proved to be inadequate. The specification was much too large. Through a series of improvements in both the design and the specification techniques we have achieved a much more compact description. This paper begins with the motivation for the design, explains the problems discovered in earlier approaches, and describes the improvements that were made. Finally, the design and its specification are explained.