Support vector machines (SVMs) are now one of the most popular machine learning techniques for solving difficult classification problems. Their effectiveness depends on two critical design decisions: 1) mapping a decision problem into an n-dimensional feature space, and 2) choosing a kernel function that maps the n-dimensional feature space into a higher dimensional and more effective classification space. The choice of kernel functions is generally limited to a small set of well-studied candidates. However, the choice of a feature set is much more open-ended without much design guidance. In fact, many SVMs are designed with standard generic feature space mappings embedded a priori. In this paper we describe a procedure for using an evolutionary algorithm to design more compact non-standard feature mappings that, for a fixed kernel function, significantly improves the classification accuracy of the constructed SVM.