A methodology for the combined acoustic detection and discrimination of explosions, which uses three discriminants, is developed for the purpose of identifying weak explosion signals embedded in complex background noise. By utilizing physical models for simple explosions that are formulated as statistical hypothesis tests, the detection/discrimination approach does not require a model for the background noise, which can be highly complex and variable in practice. Fisher’s Combined Probability Test is used to combine the p-values from all multivariate discriminants. This framework is applied to acoustic data from a 400 g explosion conducted at Los Alamos National Laboratory.