Diffusion MRI enables non-invasive in vivo reconstruction of the white matter axon bundles hereafter referred to as fascicles. DTI is known to have a hard time depicting accurately this architecture in regions where multiple fascicles cross. New multi-compartment models [1,2,3] can unravel this issue provided that the number of fascicles is known in advance. This is a model selection problem that translates to finding the optimal number of fascicles. Recently, [4] proposed to use the generalization error to choose the best model based on its ability to predict new data that has not been used for its estimation, thus avoiding the common problem of over-fitting. Despite the excellent results obtained by this method, the generalization error needs to be estimated, which is a long process that takes up to a week on high resolution data such as the recently publicly released Human Connectome Project (HCP) data [5]. In this abstract, we introduce a new model selection approach that gives results at least as good as the generalization error with a dramatically reduced computation time, making it closer to a clinical applicability.