Formal specifications of software systems need to evolve in many ways during system development. Not only are changes required to refine the specification towards an implementation, they are also required in response to changes in requirements, or to incorporate different aspects of the system, e.g., fault tolerance or timing, initially ignored in order to simplify reasoning. This paper presents anapproach for evolving Z specifications by the step-wise application of a number of simple rules. These rules not only document the specification's evolution, but also make precise how safety properties of the system evolve with the specification. Hence, reasoning about these properties performed on the original specification need not be repeated on the new specification.