We study the problem of designing support vector classifiers with respect to a Neyman-Pearson criterion. Specifically, given a user-specified level alpha, 0 < alpha < 1, how can we ensure a false alarm rate no greater than a while minimizing the miss rate? We examine two approaches, one based on shifting the offset of a conventionally trained SVM and the other based on the introduction of class-specific weights. Our contributions include a novel heuristic for improved error estimation and a strategy for efficiently searching the parameter space of the second method. We also provide a characterization of the feasible parameter set of the 2nu-SVM on which the second approach is based. The proposed methods are compared on four benchmark datasets.