One aim of this work is to investigate the feasibility of using a hierarchy of models to describe diffusion tensor magnetic resonance (MR) data in fixed tissue. Parsimonious model selection criteria are used to choose among different models of diffusion within tissue. Using this information, we assess whether we can perform simultaneous tissue segmentation and classification. Both numerical phantoms and diffusion weighted imaging (DWI) data obtained from excised pig spinal cord are used to test and validate this model selection framework. Three hierarchical approaches are used for parsimonious model selection: the Schwarz criterion (SC), the F-test t-test (F-t), proposed by Hext, and the F-test F-test (F-F), adapted from Snedecor. The F-t approach is more robust than the others for selecting between isotropic and general anisotropic (full tensor) models. However, due to its high sensitivity to the variance estimate and bias in sorting eigenvalues, the F-F and SC are preferred for segmenting models with transverse isotropy (cylindrical symmetry). Additionally, the SC method is easier to implement than the F-t and F-F methods and has better performance. As such, this approach can be efficiently used for evaluating large MRI data sets. In addition, the proposed voxel-by-voxel segmentation framework is not susceptible to artifacts caused by the inhomogeneity of the variance in neighboring voxels with different degrees of anisotropy, which might contaminate segmentation results obtained with the techniques based on voxel averaging.