Discriminative training for language recognition has been a key tool for improving system performance. In addition, recognition directly from shifted-delta cepstral features has proven effective. A recent successful example of this paradigm is SVM-based discrimination of languages based on GMM mean supervectors (GSVs). GSVs are created through MAP adaptation of a universal background model (UBM) GMM. This work proposes a novel extension to this idea by extending the supervector framework to the covariances of the UBM. We demonstrate a new SVM kernel including this covariance structure. In addition, we propose a method for pushing SVM model parameters back to GMM models. These GMM models can be used as an alternate form of scoring. The new approach is demonstrated on a fourteen language task with substantial performance improvements over prior techniques.