This paper presents a new technique for automatically generating test data. The technique is based on mutation analysis and creates test data that approximates relative adequacy. The technique is a fault-based technique that uses algebraic constraints to describe test cases designed to find particular types of faults. A set of tools, collectively called Godzilla, has been implemented that automatically generates constraints and solves them to create test cases for unit and module testing. Godzilla has been integrated with the Mothra testing system and has been used as an effective way to generate test data that kill program mutants. The paper includes an initial list of constraints and discusses some of the problems that have been solved to develop the complete implementation of the technique.