Regional analysis is normally done by fitting models per voxel and then averaging over a region, accounting for partial volume (PV) only to some degree. In thin, folded regions such as the cerebral cortex, such methods do not work well, as the partial volume confounds parameter estimation. Instead, we propose to fit the models per region directly with explicit PV modeling. In this work we robustly estimate region-wise parameters whilst explicitly accounting for partial volume effects. We use a high-resolution segmentation from a T1 scan to assign each voxel in the diffusion image a probabilistic membership to each of k tissue classes. We rotate the DW signal at each voxel so that it aligns with the z-axis, then model the signal at each voxel as a linear superposition of a representative signal from each of the k tissue types. Fitting involves optimising these representative signals to best match the data, given the known probabilities of belonging to each tissue type that we obtained from the segmentation. We demonstrate this method improves parameter estimation in digital phantoms for the diffusion tensor (DT) and ‘Neurite Orientation Dispersion and Density Imaging’ (NODDI) models. The method provides accurate parameter estimates even in regions where the normal approach fails completely, for example where partial volume is present in every voxel. Finally, we apply this model to brain data from preterm infants, where the thin, convoluted, maturing cortex necessitates such an approach.