We study the problem of designing support vector machine (SVM) classifiers that minimize the maximum of the false alarm and miss rates. This is a natural classification setting in the absence of prior information regarding the relative costs of the two types of errors or true frequency of the two classes in nature. Examining two approaches - one based on shifting the offset of a conventionally trained SVM, the other based on the introduction of class-specific weights - we find that when proper care is taken in selecting the weights, the latter approach significantly outperforms the strategy of shifting the offset. We also find that the magnitude of this improvement depends chiefly on the accuracy of the error estimation step of the training procedure. Furthermore, comparison with the minimax probability machine (MPM) illustrates that our SVM approach can outperform the MPM even when the MPM parameters are set by an oracle.