Gaussian Mixture Models are widely used nowadays, thanks to the simplicity and efficiency of the Expectation-Maximization algorithm. However, determining the optimal number of components is tricky and, in the context of data partitioning, may differ from the actual number of clusters. We propose to apply a post-processing step by means of Spectral Clustering: it allows a clever merging of similar Gaussians thanks to the Bhattacharyya distance so that clusters of any shape are automatically discovered. The proposed method shows a significant improvement compared to the classical Gaussian Mixture clustering approach and promising results against well-known partitioning algorithms with respect to the number of parameters.